Volume 7, Issue 3 (Vol.7, No.3, 2021)
mmr 2021, 7(3): 495-512 |
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Haddadi M, naser Sheykholislami S M. On dense left ideal pure $S$-acts. mmr 2021; 7 (3) :495-512
URL: http://mmr.khu.ac.ir/article-1-2766-en.html
URL: http://mmr.khu.ac.ir/article-1-2766-en.html
1- Semnan University , m.haddadi@semnan.ac.ir
2- Semnan University
2- Semnan University
Abstract: (1028 Views)
In this paper, similar to the Lembek's idea concerning a generalization of the notion of purity associated with a radical in the category of R-modules, we give the notion of purity related to a Hoehnke radical, d.l.i.pure, in the category of $S$-acts and investigate this notion. We also show that absolutely d.l.i.pure $S$-acts are exactly the $r$-weakly injective $S$-acts, for every Hoehnke radical $r$, and we give several characterization of d.l.ipure $S$-acts. We then present a closure operator induced by an $r$-dense left ideal which is closely related to the notion of d.l.i.purity and give a characterization of d.l.i.pure $S$-acts by this closure operator.
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Type of Study: Original Manuscript |
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Received: 2018/04/16 | Revised: 2022/05/7 | Accepted: 2019/12/29 | Published: 2021/12/1 | ePublished: 2021/12/1
Received: 2018/04/16 | Revised: 2022/05/7 | Accepted: 2019/12/29 | Published: 2021/12/1 | ePublished: 2021/12/1
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