Affiliation:
1. Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu University, Gaziantep, Turkey
2. Department of Mathematics, Faculty of Science, Al al-Bayt University, Al Mafraq, Jordan
Abstract
Let R be a commutative ring with a non-zero identity, S be a multiplicatively
closed subset of R and M be a unital R-module. In this paper, we define a
submodule N of M with (N :R M) ? S = ? to be weakly S-primary if there
exists s ? S such that whenever a ? R and m ? M with 0 , am ? N, then either
sa ??(N :R M) or sm ? N. We present various properties and
characterizations of this concept (especially in faithful multiplication
modules). Moreover, the behavior of this structure under module
homomorphisms, localizations, quotient modules, cartesian product and
idealizations is investigated. Finally, we determine some conditions under
which two kinds of submodules of the amalgamation module along an ideal are
weakly S-primary.
Publisher
National Library of Serbia
Reference25 articles.
1. M. Ali, Multiplication modules and homogeneous idealization II., Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 48 (2007) 321-343.
2. M. M. Ali, Residual submodules of multiplication modules, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 46 (2) (2005) 405-422.
3. F. A. Almahdi, E. M. Bouba, M. Tamekkante, On weakly S-prime ideals of commutative rings, Analele Stiintifice ale Universitatii Ovidius Constanta 29 (2) (2021) 173-186.
4. R. Ameri, On the prime submodules of multiplication modules, International journal of Mathematics and mathematical Sciences 2003 (27) (2003) 1715-1724.
5. D. D. Anderson, M. Winders, Idealization of a module, Journal of Commutative Algebra 1 (1) (2009) 3-56.