Among other things we prove that the integral closure of a Marot ring whose regular ideals are finitely generated is a Krull ring. I: 1993 Academic Press. Inc.
The Zero-Divisor Graph of a Commutative Ring
โ Scribed by David F. Anderson; Philip S. Livingston
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 121 KB
- Volume
- 217
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
โฆ Synopsis
For each commutative ring R we associate a simple graph โซ R . We investigate the interplay between the ring-theoretic properties of R and the graph-theo-ลฝ . retic properties of โซ R .
๐ SIMILAR VOLUMES
Gilmer and Heinzer proved that given a reduced ring R, a polynomial f divides a monic polynomial in R[X] if and only if there exists a direct sum decomposition of R = R0 โ . . . โ Rm (m โค deg f ), associated to a fundamental system of idempotents e0, . . . , em, such that the component of f in each
function q : U -+AS with q(u) = a, q(b) = 0, q(c) = c. Then q = a + 0 + c -a0 -ac be + abc = a + c. Corollary 2.9. If K = R a' s a field of chrircccteristl'c 0 and S is nny finite semilcctiice. each element of Qd(S) may be realized i i i IT(&').