Rings whose cyclics have finite Goldie dimension

Autor:	S. K. Jain, S. R. López-Permouth, A.H Al-Huzali
Jazyk:	angličtina
Předmět:	Noetherian Discrete mathematics Algebra and Number Theory Mathematics::Commutative Algebra Direct sum Mathematics::Rings and Algebras Injective module Horizontal line test Divisible group Injective function Combinatorics Injective hull Mathematics Resolution (algebra)
Zdroj:	Journal of Algebra. (1):37-40
ISSN:	0021-8693
DOI:	10.1016/0021-8693(92)90147-E
Popis:	A module M is said to be weakly injective if every finitely generated submodule of its injective hull E ( M ) is contained in a submodule X of E ( M ) isomorphic to M . We prove that a ring R satisfies the property that every cyclic right R -module has finite Goldie dimension if and only if every direct sum of (weakly) injective right R -modules is weakly injective. This is analog to the well-known characterization of right Noetherian rings as those for which direct sums of injective right modules are injective.
Databáze:	OpenAIRE
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