AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS | ||
| Journal of Algebraic Systems | ||
| مقاله 2، دوره 3، شماره 1، آذر 2015، صفحه 11-22 اصل مقاله (176.2 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2015.483 | ||
| نویسندگان | ||
| S. Karimzadeh* 1؛ R. Nekooei2 | ||
| 1Department of Mathematics, Vali-e-Asr University of Rafsanjan , P.O.Box 7718897111, Rafsanjan, Iran. | ||
| 2Department of Mathematics, Shahid Bahonar University of Kerman, P.O.Box 76169133, Kerman, Iran. | ||
| چکیده | ||
| In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going down theorems for modules. | ||
| کلیدواژهها | ||
| Prime submodule؛ Integral element؛ Integrally closed | ||
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آمار تعداد مشاهده مقاله: 2,103 تعداد دریافت فایل اصل مقاله: 1,577 |
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