Download or read book Simple Noetherian Rings written by John Cozzens and published by Cambridge University Press. This book was released on 2009-01-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work specifically surveys simple Noetherian rings. The authors present theorems on the structure of simple right Noetherian rings and, more generally, on simple rings containing a uniform right ideal U. The text is as elementary and self-contained as practicable, and the little background required in homological and categorical algebra is given in a short appendix. Full definitions are given and short, complete, elementary proofs are provided for such key theorems as the Morita theorem, the Correspondence theorem, the Wedderburn-Artin theorem, the Goldie-Lesieur-Croisot theorem, and many others. Complex mathematical machinery has been eliminated wherever possible or its introduction into the text delayed as long as possible. (Even tensor products are not required until Chapter 3.)
Download or read book An Introduction to Noncommutative Noetherian Rings written by K. R. Goodearl and published by Cambridge University Press. This book was released on 2004-07-12 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. New material includes the basic types of quantum groups, which then serve as test cases for the theory developed.
Download or read book Noncommutative Noetherian Rings written by John C. McConnell and published by American Mathematical Soc.. This book was released on 2001 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reprinted edition of a work that was considered the definitive account in the subject area upon its initial publication by J. Wiley & Sons in 1987. It presents, within a wider context, a comprehensive account of noncommutative Noetherian rings. The author covers the major developments from the 1950s, stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras, PI rings, differential operators, and localization theory. The book is not restricted to Noetherian rings, but discusses wider classes of rings where the methods apply more generally. In the current edition, some errors were corrected, a number of arguments have been expanded, and the references were brought up to date. This reprinted edition will continue to be a valuable and stimulating work for readers interested in ring theory and its applications to other areas of mathematics.
Download or read book Noetherian Rings and Their Applications written by Lance W. Small and published by American Mathematical Soc.. This book was released on 1987 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: ". T. Stafford -- The Goldie rank of a module " . R. Farkas -- Noetherian group rings: An exercise in creating folklore and intuition " . C. Jantzen -- Primitive ideals in the enveloping algebra of a semisimple Lie algebra " . J. Enright -- Representation theory of semisimple Lie algebras " .-E. Björk -- Filtered Noetherian rings " . Rentschler -- Primitive ideals in enveloping algebras.
Download or read book Localization in Noetherian Rings written by A. V. Jategaonkar and published by Cambridge University Press. This book was released on 1986-03-13 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph first published in 1986 is a reasonably self-contained account of a large part of the theory of non-commutative Noetherian rings. The author focuses on two important aspects: localization and the structure of infective modules. The former is presented in the opening chapters after which some new module-theoretic concepts and methods are used to formulate a new view of localization. This view, which is one of the book's highlights, shows that the study of localization is inextricably linked to the study of certain injectives and leads, for the first time, to some genuine applications of localization in the study of Noetherian rings. In the last part Professor Jategaonkar introduces a unified setting for four intensively studied classes of Noetherian rings: HNP rings, PI rings, enveloping algebras of solvable Lie algebras, and group rings of polycyclic groups. Some appendices summarize relevant background information about these four classes.
Download or read book Transcendental Division Algebras and Simple Noetherian Rings written by Richard Dean Resco and published by . This book was released on 1978 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Noetherian Rings and Rings with Polynomial Identities written by and published by . This book was released on 1979 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graduate Algebra written by Louis Halle Rowen and published by American Mathematical Soc.. This book was released on 2008 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is an expanded text for a graduate course in commutative algebra, focusing on the algebraic underpinnings of algebraic geometry and of number theory. Accordingly, the theory of affine algebras is featured, treated both directly and via the theory of Noetherian and Artinian modules, and the theory of graded algebras is included to provide the foundation for projective varieties." --Book Jacket.
Download or read book Algebra II written by A.I. Kostrikin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative alge 1 bra • Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of non-commutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry - for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the so-called microlocal analysis. The theory of operator algebras (Le.
Download or read book Advanced Algebra written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-10-11 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.
Download or read book Serial Rings written by G. Puninski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme in classical ring theory is the structure theory of rings of a particular kind. For example, no one text book in ring theory could miss the Wedderburn-Artin theorem, which says that a ring R is semisimple Artinian iffR is isomorphic to a finite direct sum of full matrix rings over skew fields. This is an example of a finiteness condition which, at least historically, has dominated in ring theory. Ifwe would like to consider a requirement of a lattice-theoretical type, other than being Artinian or Noetherian, the most natural is uni-seriality. Here a module M is called uni-serial if its lattice of submodules is a chain, and a ring R is uni-serial if both RR and RR are uni-serial modules. The class of uni-serial rings includes commutative valuation rings and closed under homomorphic images. But it is not closed under direct sums nor with respect to Morita equivalence: a matrix ring over a uni-serial ring is not uni-serial. There is a class of rings which is very close to uni-serial but closed under the constructions just mentioned: serial rings. A ring R is called serial if RR and RR is a direct sum (necessarily finite) of uni-serial modules. Amongst others this class includes triangular matrix rings over a skew field. Also if F is a finite field of characteristic p and G is a finite group with a cyclic normal p-Sylow subgroup, then the group ring FG is serial.
Download or read book Module Theory written by C. Faith and published by Springer. This book was released on 2006-11-15 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Noncommutative Ring Theory written by J.H. Cozzens and published by Springer. This book was released on 2006-11-14 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ring Theory Waterloo 1978 written by D. Handelman and published by Springer. This book was released on 2007-01-05 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ring theory conference took place at the University of Waterloo, 12-16 June 1978, and these are its proceedings. This conference was held as a part of the Summer Research Institute in Ring Theory, at Waterloo, sponsored by the Canadian Mathematical Society. In soliciting speakers, and contributors to the Proceedings, we attempted to represent those portions of ring theory which seemed to us interesting. There was thus considerable emphasis on lower K-theory and related topics, Artinian and Noetherian rings, as well as actions and representations of groups on rings. Regrettably, we could only obtain one paper in the mainstream of commutative ring theory, but we believe that the lack of quantity is more than made up for by the quality. We also took the liberty of including a survey of results in a field which we feel deserves more attention by ring theorists, C* algebras from an algebraic point of view.
Download or read book Ring Theory written by and published by Academic Press. This book was released on 1988-06-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ring Theory V1
Download or read book Integral Closure of Ideals Rings and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
