Results 141 to 150 of about 17,639 (169)

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 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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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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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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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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A note on generalizations of quasi-Frobenius rings

Asian-European Journal of Mathematics, 2016
A ring [Formula: see text] is called quasi-Frobenius, briefly QF, if [Formula: see text] is right (or left) Artinian and right (or left) self-injective. A ring [Formula: see text] is called right co-Harada if every noncosmall right [Formula: see text]-module contains a nonzero projective direct summand and [Formula: see text] satisfies the ACC on ...
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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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Some remarks on quasi-Frobenius rings

Georgian Mathematical Journal, 2015
Abstract We give some new characterizations of quasi-Frobenius rings by means of YJ-injective rings and JGP-injective rings, respectively. For example, we show that a two-sided YJ-injective right noetherian ring is quasi-Frobenius, which gives an affirmative answer to an open question asked by Roger Yue Chi Ming; a right CF, semiregular,
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Frobenius algebras and quasi-Frobenius rings

2007
Michiel Hazewinkel, Nadiya Gubareni, V.V. Kirichenko   +2 more
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