کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4587729 1334156 2008 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Commutative rings with finitely generated monoids of fractional ideals
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Commutative rings with finitely generated monoids of fractional ideals
چکیده انگلیسی

Let R be a commutative ring with identity and let P(R) be the monoid of principal fractional ideals of R. We show that P(R) is finitely generated if and only if ( the integral closure of R) is finitely generated and is finite. Moreover, is a finite direct product of finite local rings, SPIRs, Bezout domains D with P(D) finitely generated, and special Bezout rings S (S is a Bezout ring with a unique minimal prime P, SP is an SPIR, and P(S/P) is finitely generated). Also, P(R) is finitely generated if and only if F*(R), the monoid of finitely generated fractional ideals of R, is finitely generated. We show that the monoid F(R) of fractional ideals of R is finitely generated if and only if the monoid of R-submodules of the total quotient ring of R is finitely generated and characterize the rings for which this is the case.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 320, Issue 7, 1 October 2008, Pages 3006-3021