Splitting hereditary torsion theories over semiperfect rings
نویسندگان
چکیده
منابع مشابه
1-torsion of Finite Modules over Semiperfect Rings
We initiate the study of 1-torsion of finite modules over two-sided noetherian semiperfect rings. In particular, we give a criterion for determining when the 1-torsion submodule contains minimal generators of the module. We also provide an explicit construction for a projective cover of the submodule generated by the torsion elements in the top of the module. Some of the obtained results hold w...
متن کاملSemiperfect coalgebras over rings
Our investigation of coalgebras over commutative rings R is based on the close relationship between comodules over a coalgebra C and modules over the dual algebra C∗. If C is projective as an R-module the category of right C-comodules can be identified with the category σ[C∗C] of left C∗-modules which are subgenerated by C. In this context semiperfect coalgebras are described by results from mo...
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Let C be a coalgebra over a QF ring R. A left C-comodule is called strongly rational if its injective hull embeds in the dual of a right Ccomodule. Using this notion a number of characterizations of right semiperfect coalgebras over QF rings are given, e.g., C is right semiperfect if and only if C is strongly rational as left C-comodule. Applying these results we show that a Hopf algebra H over...
متن کاملOn semiperfect rings of injective dimension one
We give a characterization of right Noetherian semiprime semiperfect and semidistributive rings with inj. dimAAA 6 1.
متن کاملCharacterizations of Semiperfect and Perfect Rings(∗)
We characterize semiperfect modules, semiperfect rings, and perfect rings using locally projective covers and generalized locally projective covers, where locally projective modules were introduced by Zimmermann-Huisgen and generalized locally projective coves are adapted from Azumaya’s generalized projective covers.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1969-0244324-2