Advances in Ring TheoryKasch Modules.- Compactness in Categories and Interpretations.- A Ring of Morita Context in Which Each Right Ideal is Weakly Self-injective.- Splitting Theorems and a Problem of Müller.- Decompositions of D1 Modules.- Right Cones in Groups.- On Extensions of Regular Rings of Finite Index by Central Elements.- Intersections of Modules.- Minimal Cogenerators Over Osofsky and Camillo Rings.- Uniform Modules Over Goldie Prime Serial Rings.- Co-Versus Contravariant Finiteness of Categories of Representations.- Monomials and the Lexicographic Order.- Rings Over Which Direct Sums of CS Modules Are CS.- Exchange Properties and the Total.- Local Bijective Gabriel Correspondence and Torsion Theoretic FBN Rings.- Normalizing Extensions and the Second Layer Condition.- Generators of Subgroups of Finite Index in GLm (?G).- Weak Relative Injective M-Subgenerated Modules.- Direct Product and Power Series Formations Over 2-Primal Rings.- Localization in Noetherian Rings.- Projective Dimension of Ideals in Von Neumann Regular Rings.- Homological Properties of Color Lie Superalgebras.- Indecomposable Modules Over Artinian Right Serial Rings.- Nonsingular Extending Modules.- Right Hereditary, Right Perfect Rings Are Semiprimary.- On the Endomorphism Ring of a Discrete Module: A Theorem of F. Kasch.- Nonsingular Rings with Finite Type Dimension. |
Contents
Kasch Modules | 1 |
Compactness in Categories and Interpretations | 17 |
A Ring of Morita Context in Which Each Right Ideal is Weakly SelfInjective | 31 |
Splitting Theorems and a Problem of Muller | 39 |
Decompositions of D1 Modules | 49 |
Right Cones in Groups | 65 |
| 73 | |
Intersection Modules | 87 |
Local Bijective Gabriel Correspondence and Torsion Theoretic FBN Rings | 175 |
Normalizing Extensions and the Second Layer Condition | 191 |
Generators of Subgroups of Finite Index in GLmZG | 211 |
Weak Relative Injective MSubgenerated Modules | 221 |
Direct Product and Power Series Formation over 2Primal Rings | 239 |
Localization in Noetherian Rings | 247 |
Projective Dimension of Ideals in Von Neumann Regular Rings | 263 |
Homological Properties of Color Lie Superalgebras | 287 |
Minimal Congenerators Over Osofsky and Camillo Rings | 105 |
Uniform Modules Over Goldie Prime Serial Rings | 119 |
Co Versus Contravariant Finiteness of Categories | 129 |
Monomials and the Lexicographic Order | 145 |
Rings Over Which Direct Sums of CS Modules Are CS | 151 |
Exchange Properties and the Total | 161 |
Indecomposable Modules Over Artinian right Serial Rings | 295 |
Nonsingular Extending Modules | 305 |
Right Hereditary Right Perfect Rings Are Semiprimary | 313 |
A Theorem of F Kasch | 317 |
Nonsingular Rings with Finite Type Dimension | 322 |
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Common terms and phrases
A-injective A-mod A-tight A₁ Algebra artinian ring biregular cogenerator commutative contains contradiction Corollary cyclic defined definition denote direct product direct sum direct summand division ring element epimorphism equivalent essential right ideal essential submodule Example exists finite dimensional finite index follows functor Goldie dimension hence hereditary torsion theory homomorphism hypothesis idempotent implies injective hull injective modules integer intersection isomorphic Kasch module Krull dimension left Noetherian left R-module Lemma lex-segment Lie superalgebra linearly compact M₁ Math Mathematics meet-independent minimal module in o[M monomials morphism nilpotent Noetherian ring nonsingular ring nonzero P₁ prime ideals projective dimension Proof Proposition quotient R-Mod result right noetherian ring right Osofsky right R-module satisfies second layer condition self-injective semiprime semisimple sequence serial ring simple module Spec(R subobjects Suppose surjective T-torsionfree Theorem type submodule uniform modules uniserial weakly injective