Torsion theories over semihereditary rings
نویسندگان
چکیده
منابع مشابه
Finitely 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 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...
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Many known results on finite von Neumann algebras are generalized, by purely algebraic proofs, to a certain class C of finite Baer *-rings. The results in this paper can also be viewed as a study of the properties of Baer *-rings in the class C. First, we show that a finitely generated module over a ring from the class C splits as a direct sum of a finitely generated projective module and a cer...
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Let G be a torsion-free abelian group of type (0, 0, 0, . . . ) and R an integrally closed integral domain with quotient field K. We show that every divisorial ideal (respectively, t-ideal) J of the group ring R[X;G] is of the form J = hIR[X;G] for some h ∈ K[X;G] and a divisorial ideal (respectively, t-ideal) I of R. Consequently, there are natural monoid isomorphisms Cl(R) ∼= Cl(R[X;G]) and C...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1986
ISSN: 0263-6115
DOI: 10.1017/s1446788700026495