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Wednesday, July 22, 2020 | History

6 edition of Matrices over Commutative Rings (Pure and Applied Mathematics (Marcel Dekker)) found in the catalog.

Matrices over Commutative Rings (Pure and Applied Mathematics (Marcel Dekker))

William C. Brown

Matrices over Commutative Rings (Pure and Applied Mathematics (Marcel Dekker))

by William C. Brown

  • 122 Want to read
  • 4 Currently reading

Published by Marcel Dekker .
Written in English

    Subjects:
  • Fields & rings,
  • Science/Mathematics,
  • Algebra,
  • Rings,
  • Mathematics,
  • Applied,
  • Commutative rings,
  • Matrices

  • The Physical Object
    FormatHardcover
    Number of Pages281
    ID Numbers
    Open LibraryOL8160520M
    ISBN 100824787552
    ISBN 109780824787554

    ISBN: OCLC Number: Description: viii, pages ; 24 cm. Contents: Matrix theory over commutative rings --Free modules --The endomorphism ring of a projective module --Projective modules --Theory of a single Title: Book Description. This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module. Table of Contents. 1. Matrix Theory Over Commutative Rings 2

      Basic examples Commutative rings. The prototype example is the ring of integers with the two operations of addition and multiplication. The rational, real and complex numbers are commutative rings of a type called fields.; An algebra over a ring is itself a ring. These are also examples:(mathematics).   Matrices over commutative rings 58 77; Torsion 61 80; The structure of finitely generated modules over a PID 62 81; The theory of a single linear transformation 71 90; Application to Abelian groups 77 96; Appendix 2A: Arithmetic Lattices 77 96; Chapter 3. Simple Modules and Composition Series 81 ; Simple modules 81 ; Composition series 82

      [14] Ou S., Wang D., Yao R. Derivations of the Lie algebra of strictly upper triangular matrices over a commutative ring, Linear Algebra Appl., , (SCI) [15] Yu Q. , Wang D., Ou S. Automorphisms of the Borel subalgebras of Lie algebra of C m type over commutative rings, Linear Multilinear Algebra, , (SCI) After reminders about basic material on commutative rings, ideals and modules are extensively discussed, with applications including to canonical forms for square matrices. The core of the book discusses the fundamental theory of commutative Noetherian rings. Affine algebras over fields, dimension theory and regular local rings are also treated


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Matrices over Commutative Rings (Pure and Applied Mathematics (Marcel Dekker)) by William C. Brown Download PDF EPUB FB2

ISBN: OCLC Number: Description: viii, pages: illustrations ; 24 cm. Contents: 1. Modules Over Commutative Rings Matrices with Entries from a Commutative Ring The Ideals in M[subscript nxn](R) The Rank of a Matrix Linear Equations Minimal Primes and the Radical of an Ideal The Cayley-Hamilton Theorem Matrices over commutative rings William Brown.

Aims to cover the most important aspects of the theory of matrices whose entries come from a given commutative ring. Essential facts about commutative rings are developed throughout the book, and proofs that follow Matrices over commutative rings.

New York: Marcel Dekker, © (DLC) (OCoLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: William Matrices over Commutative Rings book Brown   I only know of a usage of Rings of Matrices over skew fields for the classification of artinian simple and semisimple rings, namely the Artin-Wedderburn theorem.

The structure of non-commutative grouprings themselves is still researched, since the module theory of those encodes the theory of representations of the group on modules over the coefficient ring of the groupring, which is occupying 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 elements in a ring, regular matrices over principal ideal rings, and regular matrices over commutative  › Books › Science & Math › Mathematics. Matrices over Commutative Rings (Chapman & Hall Pure and Applied Mathematics) 1st Edition by William Brown (Editor) ISBN ISBN Why is ISBN important.

ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book  › Books › Science & Math › Mathematics. There is a theory of determinants of matrices over non-commutative (in particular, free) rings.

It was mainly developed by Gelfand and Retah. I think the first paper is this: Gelfand, I. M., Retakh, V. Theory of noncommutative determinants, and characteristic functions of graphs. :// The main results in this paper generalize the corresponding results for matrices over commutative rings, for fuzzy matrices, for lattice matrices and for incline matrices.

View Show abstract Real algebraic geometry for matrices over commutative rings. Let S n (R):= {A ∈M n (R) | A T = A} be the set of all symmetric n × n matrices over t of S n (R) is a quadratic module if I n ∈M, M+M⊆M and A T MA⊆M for every A ∈M n (R).

e smallest quadratic module which contains a given subset G of S n (R Matrices over power series over projective rings are also discussed. These extend the known results [1, Theorem 12] and [5, Theorem 25].

Discover the world's research Linear Algebra over Commutative Rings | B. McDonald | download | B–OK. Download books for free. Find books On Linear Algebra over Commutative Rings Jos6 A. Hermida-Alonso There exists an extensive bibliography about the different problems. The book of J.

Brewer et al. [8] is a good introduction for some topics in this area and the book of E. Sontag [ ] is a good source for classical control theory. Linear Algebra over Commutative Rings REPRESENTATION OF FINITE RINGS BY MATRICES idempotent whose additive order is p, and on the following lemma: LEMMA 1 [5].

Let R be a finite, subdirectly indecomposable ring with an idempotent e Φ 0. // R is a subring of the full matrix ring over a commutative ring, then the additive order of the element e coincides with the characteristic of the ring Clean matrices over commutative rings Article (PDF Available) in Czechoslovak Mathematical Journal 59(1) March with Reads How we measure 'reads' cleanness of matrices over commutative loc al rings was extensively studied by many authors from very different view points (cf.

[1, 3, 4, 8, 9]). W e refer the reader to [11] Matrices over a Commutative Ring Pei Sheng JI∗, Xiao Ling YANG, Jian Hui CHEN School of Mathematical Sciences, Qingdao University, ShandongP. China Abstract Let Nn(R) be the algebra consisting of all strictly upper triangular n × n matrices over a commutative ring R with the identity.

An R-bilinear map φ: Nn(R)×Nn(R) −→ Nn(R)?file_no=&year_id=&quarter_id. Key words and phrases. algebra, representation theory, linear algebra, division ring, quasideterminant, biring, system of linear equations, vector space, basis manifold Abstract.

In this book I treat linear algebra over division ring. A system of linear equations over a division ring has properties similar to properties of   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   over commutative rings reduces to solvability over local rings, which are the basic building blocks of finite commutative rings. Finally, in the other direction, we show that solvability over rings with a linear order and solvability over local rings for which the maximal ideal is generated by kelements, reduces to solvability over cyclic :// 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 elements in a ring, regular matrices over principal ideal rings, and regular matrices over commutative :// /Rao/p/book/. J. Geom. Phys. 37 (), ). In fact, over the last years, we studied a lot the representation theories of $^*$-algebras over ordered rings, so this might be interesting for you.

EDIT: according to the comments, this is not really the situation you're interested in. Sorry. But I guess one can still learn something from ://Matrices Over Commutative Rings. Author(s): William C. Brown Total books are available.

And still more to come If you couldn't download the book then contact us on our email [email protected]We consider finite nilpotent groups of matrices over commutative rings.

A general result concerning the diagonalization of matrix groups in the terms of simple conditions for matrix entries is ://