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Module theory an approach to linear algebra by T. S. Blyth

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Published by Clarendon Press in Oxford [Eng.] .
Written in English


  • Modules (Algebra),
  • Vector spaces.,
  • Algebras, Linear.

Book details:

Edition Notes

Includes index.

StatementT. S. Blyth.
LC ClassificationsQA247 .B57
The Physical Object
Paginationvi, 400 p. :
Number of Pages400
ID Numbers
Open LibraryOL4539936M
ISBN 100198531621
LC Control Number77006377

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Module Theory Endomorphism rings and direct sum decompositions in some classes of modules. Authors: Facchini, Alberto Free Preview. Adds to the list of fundamental books on rings and modules ; Develops the necessary background in a logical way Author: Alberto Facchini. With their work the authors provide a solid background to module theory, accessible to anyone familiar with basic abstract algebra. 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. This concise introduction to ring theory, module theory and number theory is ideal for a first year graduate student, as well as being an excellent reference for working mathematicians in other areas. Starting from definitions, the book introduces fundamental constructions of rings and modules, as direct sums or products, and by exact by:   This book is an introduction to module theory for the reader who knows something about linear algebra and ring theory. Its main aim is the derivation of the structure theory of modules over Euclidean domains. This theory is applied to obtain the structure of abelian groups and the rational canonical.

As it was suggested before, Module Theory: An Approach to Linear Algebra by T. S. Blyth is an awesome title which covers almost every basic topic of Module theory in a very elegant, clear and efficient way. It is hands down my favorite text in the subject, but unfortunately it has been long out of print and therefore it is expensive and hard to obtain. On the one hand this book intends to provide an introduction to module theory and the related part of ring theory. Starting from a basic understand-ing of linear algebra the theory is presented with complete proofs. From the beginning the approach is categorical. On the other hand the presentation includes most recent results and includes new ones. Problem Let R be a ring with 1. A nonzero R -module M is called irreducible if 0 and M are the only submodules of M. (It is also called a simple module.) (a) Prove that a nonzero R -module M is irreducible if and only if M is a cyclic module with any nonzero element as its generator. You must have lived in England, Wales or Scotland for at least days in the last 12 months before the day you take your theory or driving test. Car and motorcycle tests cost £ When you book your test, say if you have a reading difficulty, health condition or disability.

Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. There is a certain asymmetry in this duality. While the theory of extending modules is well documented in monographs and text books, the purpose of our monograph is to. The theme, as indicated by our title, is that of modules (though our intention has not been to write a textbook purely on module theory). We begin with some group and ring theory, to set the stage, and then, in the heart of the book, develop module by: module is obtained essentially by a modest generalisation of that of a vector space, it is not surprising that it plays an important role in the theory of linear algebra. Modules are also of great importance in the higher reaches of group theory and ring theory, and are fundamental to the study of advanced topics such as homological. This expository monograph was written for three reasons. Firstly, we wanted to present the solution to a problem posed by Wolfgang Krull in [Krull 32]. He asked whether what we now call the "Krull-Schmidt Theorem" holds for ar tinian modules. The problem remained open for 63 years: its solution, a negative answer to Krull's question, was published only in (see .