Download or read book Model Theoretic Algebra With Particular Emphasis on Fields Rings Modules written by Christian.U Jensen and published by Routledge. This book was released on 2022-03-11 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume highlights the links between model theory and algebra. The work contains a definitive account of algebraically compact modules, a topic of central importance for both module and model theory. Using concrete examples, particular emphasis is given to model theoretic concepts, such as axiomizability. Pure mathematicians, especially algebraists, ring theorists, logicians, model theorists and representation theorists, should find this an absorbing and stimulating book.
Download or read book Model Theoretic Algebra written by G. Cherlin and published by Springer. This book was released on 2006-11-14 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Model Theory written by Philipp Rothmaler and published by CRC Press. This book was released on 2018-12-07 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
Download or read book Modules over Non Noetherian Domains written by László Fuchs and published by American Mathematical Soc.. This book was released on 2001 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors present both traditional and modern discoveries in the subject area, concentrating on advanced aspects of the topic. Existing material is studied in detail, including finitely generated modules, projective and injective modules, and the theory of torsion and torsion-free modules. Some topics are treated from a new point of view. Also included are areas not found in current texts, for example, pure-injectivity, divisible modules, uniserial modules, etc. Special emphasis is given to results that are valid over arbitrary domains. The authors concentrate on modules over valuation and Prüfer domains, but also discuss Krull and Matlis domains, h-local, reflexive, and coherent domains. The volume can serve as a standard reference book for specialists working in the area and also is a suitable text for advanced-graduate algebra courses and seminars.
Download or read book Algebras Rings and Modules written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2006-01-18 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accosiative rings and algebras are very interesting algebraic structures. In a strict sense, the theory of algebras (in particular, noncommutative algebras) originated fromasingleexample,namelythequaternions,createdbySirWilliamR.Hamilton in1843. Thiswasthe?rstexampleofanoncommutative”numbersystem”. During thenextfortyyearsmathematiciansintroducedotherexamplesofnoncommutative algebras, began to bring some order into them and to single out certain types of algebras for special attention. Thus, low-dimensional algebras, division algebras, and commutative algebras, were classi?ed and characterized. The ?rst complete results in the structure theory of associative algebras over the real and complex ?elds were obtained by T.Molien, E.Cartan and G.Frobenius. Modern ring theory began when J.H.Wedderburn proved his celebrated cl- si?cation theorem for ?nite dimensional semisimple algebras over arbitrary ?elds. Twenty years later, E.Artin proved a structure theorem for rings satisfying both the ascending and descending chain condition which generalized Wedderburn structure theorem. The Wedderburn-Artin theorem has since become a corn- stone of noncommutative ring theory. The purpose of this book is to introduce the subject of the structure theory of associative rings. This book is addressed to a reader who wishes to learn this topic from the beginning to research level. We have tried to write a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and related structures and will be accessible for independent study.
Download or read book Abelian Groups Module Theory and Topology written by Dikran Dikranjan and published by CRC Press. This book was released on 2019-05-31 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.
Download or read book Foundations of Module and Ring Theory written by Robert Wisbauer and published by Routledge. This book was released on 2018-05-11 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.
Download or read book Transcendence in Algebra Combinatorics Geometry and Number Theory written by Alin Bostan and published by Springer Nature. This book was released on 2021-11-02 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.
Download or read book Functor Categories Model Theory Algebraic Analysis and Constructive Methods written by Alexander Martsinkovsky and published by Springer Nature. This book was released on with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bilinear Algebra written by Kazimierz Szymiczek and published by Routledge. This book was released on 2017-11-22 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giving an easily accessible elementary introduction to the algebraic theory of quadratic forms, this book covers both Witt's theory and Pfister's theory of quadratic forms. Leading topics include the geometry of bilinear spaces, classification of bilinear spaces up to isometry depending on the ground field, formally real fields, Pfister forms, the Witt ring of an arbitrary field (characteristic two included), prime ideals of the Witt ring, Brauer group of a field, Hasse and Witt invariants of quadratic forms, and equivalence of fields with respect to quadratic forms. Problem sections are included at the end of each chapter. There are two appendices: the first gives a treatment of Hasse and Witt invariants in the language of Steinberg symbols, and the second contains some more advanced problems in 10 groups, including the u-invariant, reduced and stable Witt rings, and Witt equivalence of fields.
Download or read book Semantics of Programming Languages and Model Theory written by Manfred Droste and published by CRC Press. This book was released on 1993-09-10 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourteen papers presented at the conference on [title], held at the International Conference and Research Center for Computer Science, Schloss Dagstuhl, June 1991, as well as a few others submitted by colleagues unable to attend, reflect the interplay between algebra, logic, and semantics of programming languages. Among the topics are a formal specification of PARLOG, synthesis of nondeterministic asynchronous automata, observable modules and power domain constructions, the Smyth-completion of a quasi-uniform space, current trends in the semantics of data flow, and a theory of unary pairfunctions. Annotation copyright by Book News, Inc., Portland, OR
Download or read book Trends in Representation Theory of Algebras and Related Topics written by Andrzej Skowroński and published by European Mathematical Society. This book was released on 2008 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.
Download or read book Advances in Algebra and Model Theory written by M Droste and published by CRC Press. This book was released on 2019-08-16 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.
Download or read book Noncommutative Curves of Genus Zero written by Dirk Kussin and published by American Mathematical Soc.. This book was released on 2009-08-07 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve $\mathbb{X}$ admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain $R$ in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of $\mathbb{X}$ and the homogeneous prime ideals of height one in $R$, and these prime ideals are principal in a strong sense.
Download or read book Infinite Length Modules written by Henning Krause and published by Springer Science & Business Media. This book was released on 2000 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the role played by modules of infinite length when dealing with problems in the representation theory of groups and algebras, but also in topology and geometry; it shows the intriguing interplay between finite and infinite length modules. The volume presents the invited lectures of a conference devoted to 'Infinite Length Modules', held at Bielefeld in September 1998, which brought together experts from quite different schools in order to survey surprising relations between algebra, topology and geometry. Some additional reports have been included in order to establish a unified picture. The collection of articles, written by well-known experts from all parts of the world, is conceived as a sort of handbook which provides an easy access to the present state of knowledge and its aim is to stimulate further development.
Download or read book Elements of the Representation Theory of Associative Algebras Volume 1 written by Ibrahim Assem and published by Cambridge University Press. This book was released on 2006-02-13 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra. The self-contained treatment constitutes an elementary, up-to-date introduction to the subject using, on the one hand, quiver-theoretical techniques and, on the other, tilting theory and integral quadratic forms. Key features include many illustrative examples, plus a large number of end-of-chapter exercises. The detailed proofs make this work suitable both for courses and seminars, and for self-study. The volume will be of great interest to graduate students beginning research in the representation theory of algebras and to mathematicians from other fields.
Download or read book Theory of Generalized Inverses Over Commutative Rings written by K.P.S. Bhaskara Rao and published by CRC Press. This book was released on 2002-03-21 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. He explores regular element
