Some results on -injective modules, -flat modules and -coherent rings
Z Zhu - Commentationes Mathematicae Universitatis Carolinae, 2015 - dml.cz
Z Zhu
Commentationes Mathematicae Universitatis Carolinae, 2015•dml.czLet $ n, d $ be two non-negative integers. A left $ R $-module $ M $ is called $(n, d) $-
injective, if ${\rm Ext}^{d+ 1}(N, M)= 0$ for every $ n $-presented left $ R $-module $ N $. A
right $ R $-module $ V $ is called $(n, d) $-flat, if ${\rm Tor} _ {d+ 1}(V, N)= 0$ for every $ n $-
presented left $ R $-module $ N $. A left $ R $-module $ M $ is called weakly $ n $-$ FP $-
injective, if ${\rm Ext}^ n (N, M)= 0$ for every $(n+ 1) $-presented left $ R $-module $ N $. A
right $ R $-module $ V $ is called weakly $ n $-flat, if ${\rm Tor} _n (V, N)= 0$ for every $(n+ …
injective, if ${\rm Ext}^{d+ 1}(N, M)= 0$ for every $ n $-presented left $ R $-module $ N $. A
right $ R $-module $ V $ is called $(n, d) $-flat, if ${\rm Tor} _ {d+ 1}(V, N)= 0$ for every $ n $-
presented left $ R $-module $ N $. A left $ R $-module $ M $ is called weakly $ n $-$ FP $-
injective, if ${\rm Ext}^ n (N, M)= 0$ for every $(n+ 1) $-presented left $ R $-module $ N $. A
right $ R $-module $ V $ is called weakly $ n $-flat, if ${\rm Tor} _n (V, N)= 0$ for every $(n+ …
Let be two non-negative integers. A left -module is called -injective, if for every -presented left -module . A right -module is called -flat, if for every -presented left -module . A left -module is called weakly --injective, if for every -presented left -module . A right -module is called weakly -flat, if for every -presented left -module . In this paper, we give some characterizations and properties of -injective modules and -flat modules in the cases of or . Using the concepts of weakly --injectivity and weakly -flatness of modules, we give some new characterizations of left -coherent rings.
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