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Generalized Prime Ideal Factorization of Submodules | ||
| Journal of Algebra and Related Topics | ||
| دوره 9، شماره 2، اسفند 2021، صفحه 121-129 اصل مقاله (291.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2021.19497.1271 | ||
| نویسندگان | ||
| K. R. Thulasi* 1؛ T. Duraivel1؛ S. Mangayarcarassy2 | ||
| 1Department of Mathematics, Pondicherry University, Puducherry, India. | ||
| 2Department of Mathematics, Pondicherry Engineering College, Puducherry, India. | ||
| چکیده | ||
| In this article, we introduce generalized prime ideal factorization for all proper submodules of a finitely generated module over a Noetherian ring. We show that the generalized prime ideal factorization of a product of two coprime ideals is the product of the generalized prime ideal factorization of the ideals. We find conditions under which the generalized prime ideal factorization of a product of prime ideals is equal to the product of the prime ideals. We show that if R is a Dedekind domain, the generalized prime ideal factorization of an ideal I in R is exactly the prime ideal factorization of I. | ||
| کلیدواژه‌ها | ||
| prime submodules؛ prime filtration؛ regular prime extension filtration | ||
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