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A characterization of quasi-Frobenius rings

open access: yesA characterization of quasi-Frobenius rings
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On Annihilators and Quasi-Frobenius Rings

Lobachevskii Journal of Mathematics, 2023
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KOŞAN, MUHAMMET TAMER   +2 more
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On Pseudo-Frobenius Rings

Canadian Mathematical Bulletin, 2005
AbstractIt is proved here that a ring R is right pseudo-Frobenius if and only if R is a right Kasch ring such that the second right singular ideal is injective.
Yousif, Mohamed F.   +2 more
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Tiled Orders and Frobenius Rings

Mathematical Notes, 2002
Let \(R\) be a discrete valuation ring with quotient field \(K\) and \({\mathfrak p}:=\text{Rad\,}R\). For an \(R\)-order \(\Lambda\) in a symmetric \(K\)-algebra \(A\), the \((\Lambda,\Lambda)\)-bimodules \(\Lambda\) and \(\Lambda^*:=\hom_R(\Lambda,R)\) can be regarded as full \(R\)-lattices in \(A\).
Dokuchaev, M. A.   +2 more
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The Structure of Quasi-Frobenius Rings

Canadian Journal of Mathematics, 1974
Utilizing a matrix representation of semiperfect rings by a family of bimodules over local rings, we describe the structure of generalized quasi-Frobenius rings in two steps: a cyclic generalized quasi-Frobenius ring is a matrix ring over a cycle of Morita dualities between local rings, and an arbitrary generalized quasi-Frobenius ring is a matrix ring
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Quasi-Frobenius X-Rings

Canadian Mathematical Bulletin, 1970
In a recent study of a specific class of quasi-Frobenius rings, Feller has found it useful to introduce the X-rings ([3]). He suggested among others the following topics:(A)Determine the properties of completely indecomposable rings and matrix rings over completely indecomposable rings.(B)Determine the properties of modules over quasi-Frobenius X-rings.
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Graded (quasi-)Frobenius rings

Journal of Algebra, 2023
This work presents a study on graded Frobenius algebras from a ring theoretical perspective. To this end, the authors introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and they investigate the structure and representations of such objects.
Dăscălescu, S.   +2 more
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