Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897310 | Journal of Pure and Applied Algebra | 2018 | 16 Pages |
Abstract
Almost perfect commutative rings R are introduced (as an analogue of Bazzoni and Salce's almost perfect domains) for rings with divisors of zero: they are defined as orders in commutative perfect rings such that the factor rings R/Rr are perfect rings (in the sense of Bass) for all non-zero-divisorsrâR. It is shown that an almost perfect ring is an extension of a T-nilpotent ideal by a subdirect product of a finite number of almost perfect domains. Noetherian almost perfect rings are exactly the one-dimensional Cohen-Macaulay rings. Several characterizations of almost perfect domains carry over practically without change to almost perfect rings. Examples of almost perfect rings with zero-divisors are abundant.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
László Fuchs, Luigi Salce,