Bezout and semihereditary power series rings
نویسندگان
چکیده
منابع مشابه
Anti-archimedean Rings and Power Series Rings
We define an integral domain D to be anti-Archimedean if ⋂∞ n=1 a nD 6= 0 for each 0 6= a ∈ D. For example, a valuation domain or SFT Prüfer domain is anti-Archimedean if and only if it has no height-one prime ideals. A number of constructions and stability results for anti-Archimedean domains are given. We show that D is anti-Archimedean ⇔ D[[X1, . . .
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We next want to construct a much larger ring in which infinite sums of multiples of elements of S are allowed. In order to insure that multiplication is well-defined, from now on we assume that S has the following additional property: (#) For all s ∈ S, {(s1, s2) ∈ S × S : s1s2 = s} is finite. Thus, each element of S has only finitely many factorizations as a product of two elements. For exampl...
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We prove that each almost local-global semihereditary ring R has the stacked bases property and is almost Bézout. More precisely, if M is a finitely presented module, its torsion part tM is a direct sum of cyclic modules where the family of annihilators is an ascending chain of invertible ideals. These ideals are invariants of M. Moreover M/tM is a projective module which is isomorphic to a dir...
متن کاملFinitely presented modules over semihereditary rings
We prove that each almost local-global semihereditary ring R has the stacked bases property and is almost Bézout. More precisely, if M is a finitely presented module, its torsion part tM is a direct sum of cyclic modules where the family of annihilators is an ascending chain of invertible ideals. These ideals are invariants of M . Moreover M/tM is a projective module which is isomorphic to a di...
متن کاملON ANNIHILATOR PROPERTIES OF INVERSE SKEW POWER SERIES RINGS
Let $alpha$ be an automorphism of a ring $R$. The authors [On skewinverse Laurent-serieswise Armendariz rings, Comm. Algebra 40(1)(2012) 138-156] applied the concept of Armendariz rings to inverseskew Laurent series rings and introduced skew inverseLaurent-serieswise Armendariz rings. In this article, we study on aspecial type of these rings and introduce strongly Armendariz ringsof inverse ske...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2003
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(03)00418-6