On Bezout and Distributive Subrings of Local Rings PDF Download
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Author: Miguel Ferrero
Publisher:
ISBN:
Category : Local rings
Languages : en
Pages : 20
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Book Description
Author: Miguel Ferrero
Publisher:
ISBN:
Category : Local rings
Languages : en
Pages : 20
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Book Description
Author: A.A. Tuganbaev
Publisher: Springer Science & Business Media
ISBN: 9401150869
Category : Mathematics
Languages : en
Pages : 368
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Book Description
A module M is called distributive if the lattice Lat(M) of all its submodules is distributive, i.e., Fn(G + H) = FnG + FnH for all submodules F,G, and H of the module M. A module M is called uniserial if all its submodules are comparable with respect to inclusion, i.e., the lattice Lat(M) is a chain. Any direct sum of distributive (resp. uniserial) modules is called a semidistributive (resp. serial) module. The class of distributive (resp. semidistributive) modules properly cont.ains the class ofall uniserial (resp. serial) modules. In particular, all simple (resp. semisimple) modules are distributive (resp. semidistributive). All strongly regular rings (for example, all factor rings of direct products of division rings and all commutative regular rings) are distributive; all valuation rings in division rings and all commutative Dedekind rings (e.g., rings of integral algebraic numbers or commutative principal ideal rings) are distributive. A module is called a Bezout module or a locally cyclic module ifevery finitely generated submodule is cyclic. If all maximal right ideals of a ring A are ideals (e.g., if A is commutative), then all Bezout A-modules are distributive.
Author: Askar Tuganbaev
Publisher: CRC Press
ISBN: 9789056991920
Category : Mathematics
Languages : en
Pages : 280
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Book Description
A comprehensive introduction to the homological and structural methods of ring theory and related topics, this book includes original results as well as the most recent work in the field. It is unique in that it concentrates on distributive modules and rings, an area in which the author is recognized as one of the world's leading experts. A module is said to be distributive if the lattice of its submodules is distributive. Distributive rings are exemplified by factor rings of direct products of division rings, commutative semihereditary rings, and uniserial rings. Direct sums of distributive modules are studied in detail, as well as relations with flat modules and modules whose endomorphisms could be extended or lifted. Starting from a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. A number of exercises are also included to give further insight into the topics covered and to draw attention to relevant results in the literature. This detailed and comprehensive book will be an invaluable source of reference to researchers and specialists in this area.
Author: W. A. Rodrigues
Publisher:
ISBN:
Category : Generalized spaces
Languages : en
Pages : 56
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Author: W. A. Rodrigues
Publisher:
ISBN:
Category : Generalized spaces
Languages : en
Pages : 66
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Author: A. Giambruno
Publisher: American Mathematical Soc.
ISBN: 0821847716
Category : Mathematics
Languages : en
Pages : 283
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Book Description
Represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. This title contains results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras.
Author: Edmundo Capelas de Oliveira
Publisher:
ISBN:
Category : Integrals
Languages : en
Pages : 16
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Author: Alexander V. Mikhalev
Publisher: Springer Science & Business Media
ISBN: 9401732671
Category : Mathematics
Languages : en
Pages : 629
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Book Description
It is by no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on "our heart" might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter "Groups" to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to know in "their" chapters; interested people from other areas should be able to get a quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also enable the reader to read the "big" Handbook (Hazewinkel 1999-) and other handbooks. In case of multiple authors, the authors are listed alphabetically; so their order has nothing to do with the amounts of their contributions.
Author: Djairo Guedes de Figueiredo
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 26
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Author: Hildete Prisco Pinheiro
Publisher:
ISBN:
Category : Amino acid sequence
Languages : en
Pages : 28
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Book Description
