Results 141 to 150 of about 17,562 (171)
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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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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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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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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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The Structure of Quasi-Frobenius Rings
Canadian Journal of Mathematics, 1974Utilizing 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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Some remarks on quasi-Frobenius rings
Georgian Mathematical Journal, 2015Abstract 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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A Type of Quasi-Frobenius Ring
Canadian Mathematical Bulletin, 1967In [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, 1969In 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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Notes on quasi-Frobenius rings
Georgian Mathematical Journal, 2019Abstract We give some new characterizations of quasi-Frobenius rings. Namely, we prove that for a ring R, the following statements are equivalent: (1) R is a quasi-Frobenius ring, (2) M
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Exponent matrices and Frobenius rings
2019We give a survey of results connecting the exponent matrices with Frobenius rings. In particular, we prove that for any parmutation ?? ??? Sn there exists a countable set of indecomposable Frobenius semidistributive rings Am with Nakayama permutation ??.
Dokuchaev, M.A. +3 more
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