An Existence Results on Positive Solutions for a Remarks on k-Torsionless Modules

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SALIMI M.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2018 | Volume:4 | Issue:13 Page(s): 83-90

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Title

An Existence Results on Positive Solutions for a Remarks on k-Torsionless Modules

Author(s)

SALIMI M. | Issue Writer Certificate

Keywords

kQ1

torsionlessQ1

reflexiveQ1

MaximalQ1

CohenQ1

MacaulayQ1

Abstract

Let R be a commutative Noetherian ring. The k-torsionless modules are defined in [7] as a generalization of torsionless and reflexive modules, i. e., torsionless modules are 1-torsionless and reflexive modules are 2-torsionless. Some properties of torsionless, reflexive, and k-torsionless modules are investigated in this paper. It is proved that if M is an R-module such that G-dimR(M)<∞ , then M is k-torsionless if and only if Mp is k-torsionless for p∊ Spec(R) with depth (RP)≤ k-1, and dephRp (Mp)≥ k for p∊ Spec(R) with deph(Rp)≥ k. Furthermore, by Auslander-Bridger formula, we prove that M is k-torsionless if and only if Mp is k-torsionless for p∊ Spec(R) with depth (RP)≤ k-1, and G-dimRp(Mp)≤ depth(Rp)-k for p∊ Spec(R) with deph(Rp)≥ k. Also, it is shown that the class of Maximal Cohen-Macaulay modules and the class of k-torsionless modules are equivalent over Gorenstein local ring with dimension k. Finally, we provide the necessary and sufficient conditions which led the tensor product of k-torsionless modules to be k-torsionless.

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APA: Copy

SALIMI, M.. (2018). An Existence Results on Positive Solutions for a Remarks on k-Torsionless Modules. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 4(13 ), 83-90. SID. https://sid.ir/paper/257356/en

Vancouver: Copy

SALIMI M.. An Existence Results on Positive Solutions for a Remarks on k-Torsionless Modules. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2018;4(13 ):83-90. Available from: https://sid.ir/paper/257356/en

IEEE: Copy

M. SALIMI, “An Existence Results on Positive Solutions for a Remarks on k-Torsionless Modules,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 4, no. 13 , pp. 83–90, 2018, [Online]. Available: https://sid.ir/paper/257356/en

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