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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.
Abraham Zaks
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Approximately Mutually Unbiased Bases by Frobenius Rings
Journal of Systems Science and Complexity, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Naparat Sripaisan, Yotsanan Meemark
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A Note on Quasi-Frobenius Rings and Ring Epimorphisms [PDF]
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.
H. H. Storrer
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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,
Zhanmin Zhu
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, 2003
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. 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. Yousif
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Relative generalized Hamming weights over Frobenius rings
Indian Journal of Pure and Applied Mathematics, 2021Zihui Liu, Liu Zihui
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Demi-matroids from codes over finite Frobenius rings [PDF]
Des. Codes Cryptogr., 2015 We present a construction of demi-matroids, a generalization of matroids, from linear codes over finite Frobenius rings, as well as a Greene-type identity for rank generating functions of demi-matroids.
Thomas Britz +2 more
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On p-Ary Local Frobenius Rings and their Homogeneous Weights [PDF]
, 2016 In this work, a characterization of different properties of p-ary local Frobenius rings and their generating characters is given. Using the generating character, a general form for the homogeneous weights of such rings is described.
B. Yildiz, Makarim Abdlwahed Abdljabbar
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Notes on LCD Codes Over Frobenius Rings
IEEE Communications Letters, 2021Let $\mathcal {R}$ be a commutative Frobenius local ring. A result that the injective hull of an LCD code $\mathcal {C}$ over $\mathcal {R}$ is free of dimension $\ell (\mathcal {C})$ , where $\ell (\mathcal {C})$ is the minimum over the ...
Zihui Liu, Xinwen Wu
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On Annihilators and Quasi-Frobenius Rings
Lobachevskii Journal of Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
KOŞAN, MUHAMMET TAMER +2 more
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