This paper characterizes S-prime submodules and defines S-primary decomposition in modules, suggesting insights for UFDs and Dedekind domains.
Let F=R⁽ⁿ⁾ be a free R-module of finite rank n≥ 2 and S be a multiplicatively closed subset of R. In this paper, we characterize the S-prime submodules of F with at most n generators, when R is a UFD or a Dedekind domain. Also, we define the concept of the S-primary decomposition and give an S-primary decomposition for some submodules N of M.
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Mirzaei et al. (2025) studied this question.
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