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