Lectures on Injective Modules and Quotie
โ Carl Faith
๐ Library
๐
1967
๐ Springer
๐ English
โฆ LIBER โฆ
๐
Injective Modules and Injective Quotient Rings
โ Scribed by Carl Faith (Author)
- Publisher
- CRC Press
- Year
- 1982
- Leaves
- 120
- Edition
- 1
- Category
- Library
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No coin nor oath required. For personal study only.
โฆ Synopsis
First published in 1982. These lectures are in two parts. Part I, entitled injective Modules Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E,R) of right ideals annihilated by subsets of E. Part II is on the subject of (F)PF, or (finitely) pseudo-Frobenius, rings [i.e., all (finitely generated) faithful modules generate the category mod-R of all R-modules]. (The PF rings had been introduced by Azumaya as a generalization of quasi-Frobenius rings, but FPF includes infinite products of Prufer domains, e.g., Z w .)
โฆ Table of Contents
Injective modules.- Essential extensions and the injective hull.- Quasi-Injective modules.- Radical and semiprimitivity in rings.- The endomorphism ring of a quasi-injective module.- Noetherian, artinian, and semisimple modules and rings.- Rational extensions and lattices of closed submodules.- Maximal quotient rings.- Semiprime rings with maximum condition.- Nil and singular ideals under maximum conditions.- Structure of noetherian prime rings.- Maximal quotient rings.- Quotient rings and direct products of full linear rings.- Johnson rings.- Open problems.
โฆ Subjects
Mathematics & Statistics;Advanced Mathematics;Algebra
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