Envelopes of commutative rings |
| |
Authors: | Rafael Parra Manuel Saorín |
| |
Institution: | [1]Departamento de Cdlculo. Escuela Bdsica, Facultad de Ingenieria, Universidad de los Andes, Aptdo. 5101, Merida, Venezuela [2]Departamento de Matemdticas, Universidad de Murcia, Aptdo. 4021, 30100 Espinardo, Murcia, Spain |
| |
Abstract: | Given a significative class ℱ of commutative rings, we study the precise conditions under which a commutative ring R has an ℱ-envelope. A full answer is obtained when ℱ is the class of fields, semisimple commutative rings or integral domains. When ℱ is the class of Noetherian rings, we give a full answer when the Krull dimension of R is zero and when the envelope is required to be epimorphic. The general problem is reduced to identifying the class of non-Noetherian
rings having a monomorphic Noetherian envelope, which we conjecture is the empty class. |
| |
Keywords: | Noetherian ring envelope local ring artinian ring Krull dimension |
本文献已被 CNKI 维普 SpringerLink 等数据库收录! |
|