Results 91 to 100 of about 123 (113)
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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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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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Gauss Sums over Quasi-Frobenius Rings
2001Quasi-Frobenius (QF) rings comprise finite fields, Galois rings and enjoy remarkable character-theoretic properties. We define two types of Gauss sums over QF rings: complete and incomplete. We compute the modulus of the former. We estimate the modulus of the latter from above and give an application to Gauss sums over Galois rings.
Philippe Langevin, Patrick Solé
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Frobenius and Quasi-Frobenius Rings
1999The 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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Some characterizations of quasi-Frobenius rings
Bollettino dell'Unione Matematica Italiana, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A note on generalizations of quasi-Frobenius rings
Asian-European Journal of Mathematics, 2016A 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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