Noncommutative Ring Theory: Papers Presented at the Internation Conference held at Kent State University April 4-5, 1975J.H. Cozzens, F.L. Sandomierski |
Contents
| 1 | |
ZERODIVISORS IN TENSOR PRODUCTS | 32 |
REGULAR RINGS AND RANK FUNCTIONS | 83 |
SOME ASPECTS OF NONCOMMUTATIVE NOETHERIAN RINGS | 105 |
CERTAIN INJECTIVES ARE ARTINIAN | 128 |
ARTINIAN QUOTIENT RINGS OF MACAULAY RINGS | 140 |
CYCLIC AND FAITHFUL OBJECTS IN QUOTIENT CATEGORIES | 151 |
PRIME SINGULARSPLITTING RINGS WITH | 173 |
PROBLEM SESSION ON REGULAR RINGS | 195 |
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Common terms and phrases
A₁ A₂ Artinian ring B₂ bilinear system bounded Noetherian ring C-cyclic C-primary chief factors cofaithful cogenerator comp condition Corollary critical module cyclic defined denote direct sum directly finite division algebra elements embedded equivalent exists factor ring finite length finite-dimensional finitely generated module follows fully bounded Noetherian functor Goldie ring Hence implies injective isomorphic K-algebra Krull dimension left ideal left Noetherian left R-module Lemma Math maximal torsion radical maximal two-sided ideal minimal prime ideal nilpotent Noetherian ring nonsingular primary decomposition prime ring prime splitting ring Proof proper torsion Proposition pseudo-rank function quotient ring R-module rank function regular ring result right FBN ring right R-module satisfies semigroup semiprime short exact sequence simple Artinian simple ring spec subidealizer tensor product Theorem torsion preradical torsionfree two-sided ideal zero right socle zero-divisors σ σ