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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
Bruno J. Müller
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On Annihilators and Quasi-Frobenius Rings

Lobachevskii Journal of Mathematics, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
KOŞAN, MUHAMMET TAMER, Quynh, Troung Cong, Nhan, Tran Hoai Ngoc   +2 more
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Quasi-Frobenius Rings

, 2003
Provides an elementary account of the basic facts about quasi-Frobenius ...
W. K. Nicholson, M. F. Yousif
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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., Zhou, Yiqiang, Zeyada, Nasr   +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., Kirichenko, V. V., Chernousova, Zh. T.   +2 more
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A Type of Quasi-Frobenius Ring

Canadian Mathematical Bulletin, 1967
In [3], the author proved that a ring R with identity is right noetherian and right injective if and only if R is a direct sum of a finite number of uniform right ideals, which are completely primary in the sense of that paper. In this paper, we shall determine the structure of such rings in the case where the sum of the isomorphic uniform components ...
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Frobenius and Quasi-Frobenius Rings

1999
The class of rings that are self-injective (as a left or right module over themselves) has been under close scrutiny by ring theorists. There is a vast literature on the structure of self-injective rings satisfying various other conditions. In a book of limited ambition such as this, it would be difficult to do justice to this extensive literature.
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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., Năstăsescu, C., Năstăsescu, L.   +2 more
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MORE ON QUASI-FROBENIUS RINGS

Mathematics of the USSR-Sbornik, 1973
Let be a ring and its Jacobson radical. Let us set , , and if is a limit ordinal. We call a ring an annihilating ring if the left (right) annihilator of the right (left) annihilator of an arbitrary left (right) ideal is itself. We prove that a ring is quasi-Frobenius if and only if it is a left self-injective annihilating ring and for some ...
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A Note on Quasi-Frobenius Rings and Ring Epimorphisms

Canadian Mathematical Bulletin, 1969
In this note, we characterize quasi-Frobenius rings by a weakened form of the usual condition, that every ideal is an annihilator ideal.We then apply this result to pure rings in the sense of Cohn and to dominant rings, a concept arising in the study of ring epimorphisms. All rings considered have a unit element.
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