کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4587729 | 1334156 | 2008 | 16 صفحه PDF | دانلود رایگان |

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.
Journal: Journal of Algebra - Volume 320, Issue 7, 1 October 2008, Pages 3006-3021