Results 81 to 90 of about 123 (113)

New Characterizations of Quasi-Frobenius Rings

Communications in Algebra, 2006
In this article, we give several new characterizations of Quasi-Frobenius rings by using mininjectivity, simple injectivity, and small injectivity, respectively. Several known results on Quasi-Frobenius rings are reproved as corollaries.
Liang Shen, Jianlong Chen
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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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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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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 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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New characterizations of quasi-Frobenius rings

Asian-European Journal of Mathematics, 2023
In this paper, we firstly provide several new characterizations of quasi-Frobenius rings by using some generalized injectivity of rings with certain chain conditions. For example, [Formula: see text] a ring [Formula: see text] is quasi-Frobenius if and only if [Formula: see text] is right [Formula: see text], right minfull with ACC on right ...
Thuyet, Le Van, Diallo, Abdoul Djibril, Diop, Papa Cheikhou, Quynh, Truong Cong   +3 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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On Quasi-Frobenius Rings

2001
There are three outstanding conjectures about quasi-Frobenius rings: The Faith conjecture that every left perfect, right selfinjective ring is quasi-Frobenius; The FGF-conjecture that every ring for which each finitely generated right module embeds in a free module is quasi-Frobenius; and The Faith-Menal conjecture that every right noetherian ring in ...
W. K. Nicholson, M. F. Yousif
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Quasi-Frobenius Rings and Nakayama Permutations of Semiperfect Rings

Ukrainian Mathematical Journal, 2002
An associative ring \(A\) is called a ring with duality for simple modules (or a DSM-ring) if for each simple right (left) \(A\)-module \(U\) the dual module \(U^*\) is a simple left (right) \(A\)-module. It is known that an Artinian ring is quasi-Frobenius iff it is a DSM-ring.
Dokuchaev, M.A., Kirichenko, V.V.
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Quasi-Frobenius Rings

1976
A ring A is quasi-Frobenius (QF) in case A is right and left Artinian, and there exists an A-duality fin. gen. mod-A ↝ fin. gen. A-mod.
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