Download or read book Rings Close to Regular written by A.A. Tuganbaev and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface All rings are assumed to be associative and (except for nilrings and some stipulated cases) to have nonzero identity elements. A ring A is said to be regular if for every element a E A, there exists an element b E A with a = aba. Regular rings are well studied. For example, [163] and [350] are devoted to regular rings. A ring A is said to be tr-regular if for every element a E A, there is an element n b E A such that an = anba for some positive integer n. A ring A is said to be strongly tr-regular if for every a E A, there is a positive integer n with n 1 n an E a + An Aa +1. It is proved in [128] that A is a strongly tr-regular ring if and only if for every element a E A, there is a positive integer m with m 1 am E a + A. Every strongly tr-regular ring is tr-regular [38]. If F is a division ring and M is a right vector F-space with infinite basis {ei}~l' then End(MF) is a regular (and tr-regular) ring that is not strongly tr-regular. The factor ring of the ring of integers with respect to the ideal generated by the integer 4 is a strongly tr-regular ring that is not regular.
Download or read book Near rings The Theory and its Applications written by and published by Elsevier. This book was released on 2011-10-10 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: Near-rings: The Theory and its Applications
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 Rings Close to Regular and Reduced written by Weixing Chen and published by . This book was released on 2006 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rings Close to Regular written by Askar Tuganbaev and published by . This book was released on 2014-01-15 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Regular Rings and Strongly Regular Rings written by Jew-Chen Hwang and published by . This book was released on 1973 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Von Neumann Regular Rings written by K. R. Goodearl and published by Pitman Publishing. This book was released on 1979 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Properties of Regular Rings written by Mignon Riley and published by . This book was released on 1967 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Properties of Regular Rings by Mathews C Waddell a Dissertation 1950 written by Mathews C. Waddell and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Radical Theory of Rings written by J.W. Gardner and published by CRC Press. This book was released on 2003-11-19 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Radical Theory of Rings distills the most noteworthy present-day theoretical topics, gives a unified account of the classical structure theorems for rings, and deepens understanding of key aspects of ring theory via ring and radical constructions. Assimilating radical theory's evolution in the decades since the last major work on rings and radicals was published, the authors deal with some distinctive features of the radical theory of nonassociative rings, associative rings with involution, and near-rings. Written in clear algebraic terms by globally acknowledged authorities, the presentation includes more than 500 landmark and up-to-date references providing direction for further research.
Download or read book On Properties of Regular Rings written by Mathews Cary Waddell and published by . This book was released on 1950 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Rings written by Neal Henry McCoy and published by . This book was released on 1969 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Radical and Semisimple Classes of Rings written by Richárd Wiegandt and published by Kingston, Ont. : Queen's University. This book was released on 1974 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Weakly Regular Rings written by James Curtis Rewalt and published by . This book was released on 1974 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Regular Overrings of Regular Local Rings written by Judith D. Sally and published by . This book was released on 1971 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Extensions of Rings and Modules written by Gary F. Birkenmeier and published by Springer Science & Business Media. This book was released on 2013-07-19 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: The "extensions" of rings and modules have yet to be explored in detail in a research monograph. This book presents state of the art research and also stimulating new and further research. Broken into three parts, Part I begins with basic notions, terminology, definitions and a description of the classes of rings and modules. Part II considers the transference of conditions between a base ring or module and its extensions. And Part III utilizes the concept of a minimal essental extension with respect to a specific class (a hull). Mathematical interdisciplinary applications appear throughout. Major applications of the ring and module theory to Functional Analysis, especially C*-algebras, appear in Part III, make this book of interest to Algebra and Functional Analysis researchers. Notes and exercises at the end of every chapter, and open problems at the end of all three parts, lend this as an ideal textbook for graduate or advanced undergradate students.
Download or read book Investigation of Properties of Regular Rings written by Bettie Green Wallace and published by . This book was released on 1965 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
