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Thursday, August 6, 2020 | History

2 edition of Associative rings and the Whitehead property of modules found in the catalog.

Associative rings and the Whitehead property of modules

Jan Trlifaj

Associative rings and the Whitehead property of modules

by Jan Trlifaj

  • 285 Want to read
  • 9 Currently reading

Published by Verlag Reinhard Fischer in München .
Written in English

    Subjects:
  • Algebra, Homological,
  • Modules (Algebra),
  • Rings (Algebra)

  • Edition Notes

    StatementJan Trlifaj.
    SeriesAlgebra Berichte -- Nr. 63
    ContributionsKasch, F. 1921-, Pareigis, Bodo
    The Physical Object
    Paginationvi, 40 p. --
    Number of Pages40
    ID Numbers
    Open LibraryOL18447578M
    ISBN 103889270654

    By Huynh and Rizvi (J. Algebra () ; Characterizing rings by a direct decomposition property of their modules, preprint ) rings over which every countably generated right module. D-module course requires some background in non-commutative algebra. Such a background is given below. Filtered rings and modules. Let Abe an associative ring with unit. We call Aa filtered ring if an increasing filtration A i⊂A i+1 ⊂ by additive subgroups is given such that .

    Skew fields of fractions, and the prime spectrum of a general ring --Balanced rings --Modules finite over endomorphism ring --The cancellation property for modules --The structure of noetherian rings --Quasisimple modules and other topics in ring theory --Blocks and centers of group algebras --Closure spaces with applications to ring theory. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature.

    A (right R-) module N is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module M, Ext R(M,N) = 0 implies M is projective. Dually, i-test modules. Modules decomposed into a direct sum of distributive modules and rings that are a direct sum of distributive right ideals were studied in[, , 22, , 91, 80, ].


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Associative rings and the Whitehead property of modules by Jan Trlifaj Download PDF EPUB FB2

Additional Physical Format: Online version: Trlifaj, Jan. Associative rings and the Whitehead property of modules. München: R. Fischer, (OCoLC) Associative rings and the Whitehead property of modules by Jan Trlifaj Paperback, 40 Pages, Published No copies of this book were found in stock from online book stores and marketplaces.

Alert me when this book becomes available. Home | iPhone App | Sell Books Pages: Associative rings and the Whitehead property of modules [Abstract of thesis] By Jan Trlifaj Topics: mscD80, mscK99Author: Jan Trlifaj.

We compute the Whitehead groups of the associative rings in a class which includes (twisted) formal power series rings and the augmentation localizations of group rings and polynomial rings Author: Desmond Sheiham.

We compute the Whitehead groups of the associative rings in a class which includes (twisted) formal power series rings and the augmentation localizations of group rings and polynomial rings.

For any associative ring A, we obtain an invariant of a pair (P, α), where P is a finitely generated projective A -module and α:P→P is an Cited by: 7. Dissertation: Associative rings and the Whitehead property of modules (in Czech) Mathematics Subject Classification: 16—Associative rings and algebras Advisor 1: Ladislav Bican.

This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal.

of finitely generated projective R-modules. We will then have to prove that these topologically defined groups agree with the definition of K0(R) in chapter II, as well as with the classical constructions of K1(R) and K2(R) in this chapter.

The Whitehead Group K1 of a ring Let Rbe an associative ring with unit. Identifying each n. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings.

Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Read the latest chapters of Handbook of Algebra atElsevier’s leading platform of peer-reviewed scholarly literature.

Ek l o f, Whitehead modules (3; 23 pp.) Goldie’s theorem, Noetherian rings and related rings Sheaves in ring theory A.A. Tuganbaev, Modules with the exchange property and exchange rings (2; 25 pp.) xiv Outline of the series A.A.

Nechaev, Finite rings with applications (5; pp.) T.Y. Lam, Hamilton’s quaternions (3; 26 pp. More generally, for any A ∞ A_\infty-ring spectrum R R, there is a notion of R R-module spectra forming a category Mod R Mod_R, which in turn carries an associative and commutative smash product ∧ R \wedge_R and a model category structure on Mod R Mod_R such that ∧ R \wedge_R becomes unital in the homotopy category.

The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules.

In particular, matrix CS-rings are studied and clear proofs of fundamental decomposition results on CS-modules over commutative domains are given. Algebraic K-theory describes a branch of algebra that centers about two functors.

K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups.

Just as functors K0 and K1 are important to geometric topologists, K2 is. It has order 2. The quotient group is called the reduced Whitehead group of the ring.

Let be a multiplicative group and let be its group ring is a natural homomorphism coming from the inclusion quotient group is called the Whitehead group of the group. Given a homomorphism of groups, there is a natural induced homomorphism, such that for.

A ring object in a category with finite products is triple where the pair is a commutative group object and the operation is associative.

A connected ring can be defined as a ring with unit such that it induces an isomorphism in degree zero. There are two preliminaries needed for the construction of the group ring. 4 CONTENTS 4 Associative Algebras and Their Modules Associative Algebras The cancellation property for modules.- The structure of noetherian rings.- Quasisimple modules and other topics in ring theory.- Blocks and centers of group algebras.- Closure spaces with applications to ring theory.- On Goldman's primary decomposition.

Series Title: Lecture notes in mathematics, Responsibility: Tulane University Ring and. J. 39 (). Trlifaj, Associative rings and the Whitehead property of modules, Algebra Berichte, Vol.

63, Verlag R. Fischer (). [ J. Trlifaj, ~m Neumann regular rings and the Whitehead property of modules, Comment. EXERCISES AND SOLUTIONS IN GROUPS RINGS AND FIELDS 5 that (y(a)a)y(a)t= ethen (y(a)a)e= e Hence y(a)a= e:So every right inverse is also a left inverse. Now for any a2Gwe have ea= (ay(a))a= a(y(a)a) = ae= aas eis a right identity.

Hence eis a left identity. If Gis a group of even order, prove that it has an element a6=esatisfying a2 = e. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem.

The class of rings and modules with extending properties (i.e. CS, max CS, min CS, max-min CS) is an important class in ring and module theory. It attracts a lot of interest among ring theorists.

Let R be an associative ring with identity and M, a right R− module. We prove that for a finitely generated, quasi-projective which is a self.Skew fields of fractions and the prime spectrum of a general ring --Balanced rings --Modules finite over endomorphism ring --The cancellation property for modules --The structure of noetherian rings --Quasisimple modules and other topics in ring theory --Blocks and centers of group algebras --Closure spaces with applications to ring theory --On.