Address: Department of Mathematics, Faculty of Science, Payame Noor University, Tehran, Iran
E-mail: Sha.Rezaei@gmail.com
Abstract: Let $I$ be an ideal of Noetherian ring $R$ and $M$ a finitely generated $R$-module. In this paper, we introduce the concept of weakly colaskerian modules and by using this concept, we give some vanishing and finiteness results for local homology modules. Let $I_{M}:=_{R}(M/IM)$, we will prove that for any integer $n$ (i) If $N$ is a weakly colaskerian linearly compact $R$-module such that $(0:_N {I_M})\ne 0$ then \[ _{I_M}(N)= \inf \lbrace i\mid _i^{I_M}(N)\ne 0 \rbrace =\inf \lbrace i \mid _i^I(M,N)\ne 0 \rbrace \,. \] (ii) If $(R,)$ is a Noetherian local ring and $N$ is an artinian $R$-module then \cup _{i<n}_R\big (_i^{I_M}(N)\big )=\cup _{i<n}_R\big (_i^I(M,N)\big )=\\ \cup _{i<n}_R\big (_i^R(M/IM,N)\big )\,, \inf \lbrace i \mid _i^{I_M}(N) \text{is} \text{not} \text{Noetherian} Rbad hbox \rbrace =\\ \inf \lbrace i \mid _i^I(M,N) \mbox {\ is not Noetherian R-module\,}\rbrace \,.
AMSclassification: primary 13D45; secondary 16E30.
Keywords: coregular sequence, local homology, weakly colaskerian.
DOI: 10.5817/AM2020-1-31