Results 11 to 20 of about 18,020 (162)
A Griesmer bound for linear codes over finite quasi-Frobenius rings
Discrete Applied Mathematics, 2003 In this article we give a Griesmer type bound for linear codes over finite quasi-Frobenius rings and consider linear codes over these rings meeting the bound. And we study a geometrical characterization of linear codes over finite chain rings meeting the
Keisuke Shiromoto, L Storme
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MacWilliams extending conditions and quasi-Frobenius rings [PDF]
Journal of Algebra, 2022 . MacWilliams proved that every finite field has the extension property for Hamming weight which was later extended in a seminal work by Wood who characterized finite Frobenius rings as precisely those rings which satisfy the MacWilliams extension property.
P. A. Guil Asensio, A. K. Srivastava
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On Gray Images of Cyclic and Self-Orthogonal Codes over
EntropyLet p be a prime with p∉{2,5} and let q=pm. This paper studies cyclic and self-orthogonal linear codes of length n over the finite local non-Frobenius ring Rp,u,v=Fq+uFq+vFq, u2=v2=uv=vu=0.
Sami H. Saif, Alhanouf Ali Alhomaidhi
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Injective classical quotient rings of polynomial rings are quasi-Frobenius
Journal of Pure and Applied Algebra, 1993 Let \(R\) be a ring and let \(X\) be a set of central indeterminates. The type of problem considered is the following: If the classical left quotient ring of \(R[X]\) exists and is left or right self-injective, does the left quotient ring of \(R\) exist and satisfy the corresponding property?
Herbera, Dolors, Pillay, Poobhalan
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A note on quasi-Frobenius rings [PDF]
Proceedings of the American Mathematical Society, 1996 It is shown that a semiperfect ring R R is quasi-Frobenius if and only if every closed submodule of
Dinh Van Huynh, Ngo Si Tung
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A characterization of quasi-Frobenius rings
Osaka Mathematical Journal, 1952 It is shown that a ring \(A\) with unit element and satisfying minimum condition is a quasi-Frobenius ring [the reviewer, Ann. Math. (2) 42, 1--21 (1941; Zbl 0026.05801)] if and only if it satisfies the following condition proposed by \textit{K. Shoda} [Proc. Japan. Acad.
M. Ikeda
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Two characterizations of quasi-Frobenius rings [PDF]
Pacific Journal of Mathematics, 1969 E. Rutter
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Remarks on quasi-Frobenius rings
Illinois Journal of Mathematics, 1958 J. Dieudonne
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Journal of Mathematics, 2023 Let A be a class of some right R-modules that is closed under isomorphisms, and let M be a right R-module. Then M is called A-D3 if, whenever N and K are direct summands of M with M=N+K and M/K∈A, then N∩K is also a direct summand of M; M is called an A ...
Zhanmin Zhu
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Generalizations of the theory of quasi-frobenius rings [PDF]
In this thesis, we consider several generalizations of the theory of Quasi-Frobenius rings, and construct examples of the classes of rings we introduce. In Chapter 1 we establish well known results, although the way in which we use idempotents is apparently new.\ud \ud Chapter 2 is devoted to the study of three generalizations of Quasi-Frobenius rings,
Norton, Nicholas Charles
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