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Injective Modules and Injective Quotient Rings

Faith
€229.40
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A01=Carl Faith
A01=Faith
advanced module classification
Age Group_Uncategorized
Age Group_Uncategorized
annihilator conditions
Artinian Ring
Author_Carl Faith
Author_Faith
automatic-update
Category1=Non-Fiction
Category=PBF
chain conditions in algebra
Commutative Ring
COP=United Kingdom
Delivery_Pre-order
Dense Submodule
Direct Sum
Direct Summand
Endomorphism Ring
eq_isMigrated=2
eq_nobargain
Essential Left Ideal
Finite Goldie Dimension
Fitting-Krull-Schmidt lemma
Indecomposable Direct Summand
Indecomposable Injective
Indecomposable Modules
Injective Hull
Injective Module
injective module E
injective quotient rings
Kasch Ring
Language_English
Levitzki Rings
module theory
Morita Duality
Noetherian Ring
noncommutative ring theory
PA=Temporarily unavailable
PF Ring
Price_€100 and above
PS=Active
pseudo-Frobenius rings
Quasi-injective Module
ring homomorphisms
Self-injective Ring
Semihereditary Ring
Semiperfect Ring
Semiprimary Ring
Simple Left Ideal
softlaunch

Product details

  • ISBN 9781138401877
  • Weight: 380g
  • Dimensions: 178 x 254mm
  • Publication Date: 18 Dec 2020
  • Publisher: Taylor & Francis Ltd
  • Publication City/Country: GB
  • Product Form: Hardback
  • Language: English
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Description

Injective Modules and Injective Quotient Rings, in two parts, is the only book of its kind to combine commutative and noncommutative ring theory. This unique and outstanding contribution to the mathematical literature will immediately advance the studies of mathematicians and graduate students in the field.

Written by a leading expert in the field, Injective Modules and Injective Quotient Rings offers readers the key concepts and methods used in both noncommutative and commutative ring theory. Part I provides the first non-torsion-theory proof of the Teply-Miller theorem and the first statement and proof of the converse of the Teply-Miller-Hansen theorem. Many applications of these theorems to the structure of rings and modules are given, including generalizations of theorems of Cailleau-Beck and Matlis on the structure of ∑-injectives and commutative rings. Part II provides an alternative approach to the solution of Kaplansky's problem on the classification of FGC rings. Of particular importance is the consistent use of noncommutative ring theoretical techniques throughout Part II to obtain theorems lying purely in the domain of commutative ring theory.

Graduate students and mathematicians in both commutative and noncommutative ring theory will learn from the unique approach and new general methods in ring theory contained in Injective Modules and Injective Quotient Rings.
About Carl Faith | Faith
Carl Faith is Professor of Mathematics at Rutgers University, New Brunswick, New Jersey. He graduated from the University of Kentucky with honors in mathematics in 1951, and received his Ph.D. from Purdue University in 1955. In 1959-1960 he was NATO post-doctoral fellow at Heidelberg University. Professor Faith taught at several major academic institutions, including Purdue University, Michigan State University, and Pennsylvania State University, and he was also an NSF postdoctoral fellow and a member of the Institute for Advanced Study before he joined Rutgers in 1962. In 1970, he attended a portion of Tulane University's Algebra Year, and in 1965-1966 he was a visiting scholar at the University of California at Berkeley. He has lectured extensively in Europe and India. An author of numerous publications, including 5 books, Professor Faith's re­search interests are in ring theory, module theory, and Galois theory. He is a member of the American Mathematical Society and the Association of Members of the Institute for Advanced Study.

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