Chiang Mai Journal of Science

Print ISSN: 0125-2526 | eISSN : 2465-3845

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On Quasi-Primary Submodules

Shahabaddin E. Atani* and Ahmad Y. Darani
* Author for corresponding; e-mail address: ebrahimi@guilan.ac.ir
Volume: Vol.33 No.3 (SEPTEMBER 2006)
Research Article
DOI:
Received: 4 January 2006, Revised: -, Accepted: 3 July 2006, Published: -

Citation: Atani S.E. and Darani A.Y., On Quasi-Primary Submodules, Chiang Mai Journal of Science, 2006; 33(3): 249-254.

Abstract

Let  R be a commutative ring with non-zero identity. We define a proper submodule Nof an  R -module M to be quasi-primary if  rad(N :RM) = P is a prime ideal of  R. In this case we also say that N is a P-quasi-primary submodule of M. A number of results concerning quasi-primary submodules are given. For example, we show that over a Prüfer domain of finite character  R , every non-zero R-submodule of a module M is the intersection of  finite number of  quasi-primary submodules with incomparable radicals.

Keywords: quasi-primary, multiplication, secondary

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