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MAX-INJECTIVE, MAX-FLAT MODULES AND MAX-COHERENT RINGS
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 Title & Authors
MAX-INJECTIVE, MAX-FLAT MODULES AND MAX-COHERENT RINGS
Xiang, Yueming;
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 Abstract
A ring R is called left max-coherent provided that every maximal left ideal is finitely presented. (resp. ) denotes the class of all max-injective left R-modules (resp. all max-flat right R-modules). We prove, in this article, that over a left max-coherent ring every right R-module has an -preenvelope, and every left R-module has an -cover. Furthermore, it is shown that a ring R is left max-injective if and only if any left R-module has an epic -cover if and only if any right R-module has a monic -preenvelope. We also give several equivalent characterizations of MI-injectivity and MI-flatness. Finally, -dimensions of modules and rings are studied in terms of max-injective modules with the left derived functors of Hom.
 Keywords
max-injective (pre)cover;max-flat preenvelope;max-coherent ring;MI-injective module;MI-flat module;-dimension;
 Language
English
 Cited by
1.
Neat-flat Modules, Communications in Algebra, 2016, 44, 1, 416  crossref(new windwow)
2.
Absolutelys-Pure Modules and Neat-Flat Modules, Communications in Algebra, 2015, 43, 2, 384  crossref(new windwow)
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