Results 1 to 10 of about 86 (83)
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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On Almost Quasi-Frobenius Fuzzy Rings
مجلة بغداد للعلوم, 2004 In this paper, we introduce the concept of almost Quasi-Frobcnius fuzzy ring as a " " of Quasi-Frobenius ring. We give some properties about this concept with qoutient fuzzy ring. Also, we study the fuzzy external direct sum of fuzzy rings.
Baghdad Science Journal
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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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A Generalization of Quasi-Frobenius Rings [PDF]
Proceedings of the American Mathematical Society, 1969 Let \(R\) be a ring and \(_R\mathcal M\) the category of all left \(R\)-modules. \textit{G. Azumaya} [Nagoya Math. J. 27, 697--708 (1966; Zbl 0144.02303)] proved that if all faithful left \(R\)-modules are generators in \(_R\mathcal M\), \(R\) is left self-injective and a direct sum of indecomposable left ideals having minimal left ideals (cf.
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Some results on quasi-Frobenius rings [PDF]
Commentationes Mathematicae Universitatis Carolinae, 2017 Summary: We give some new characterizations of quasi-Frobenius rings by the generalized injectivity of rings. Some characterizations give affirmative answers to some open questions about quasi-Frobenius rings, and some characterizations improve some results on quasi-Frobenius rings.
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A note on quasi-Frobenius rings [PDF]
Pacific Journal of Mathematics, 1968 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Filtered quasi-Frobenius rings
Mathematische Zeitschrift, 1968 The main object of this note is to prove that a filtered ringA is quasi-Frobenius, if its associated graded ring E ~ (A) is quasi-Frobenius (Theorem 1). In w 1, we discuss some generalities on quasi-Frobenius rings. In w 2, given a filtered ring A such that F~A=A for some n, we construct an injective, filtered Amodule F* such that E ~ (F*) is E ~ (A ...
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Quasi-Frobenius quotient rings of group rings [PDF]
Journal of the Australian Mathematical Society, 1975 The purpose of this paper is an extension of a theorem of Hughes (1973). He showed: Let R be a ring which has a right artinian right quotient ring and let G be a group which has a (transfinite) ascending normal series with each factor either finite or cyclic, but only a finite number of finite factors.
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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 R ( ω ) R(\omega ) is non-small, where R ( ω ) R(\omega ) denotes the direct sum of ω \omega copies of the right ...
Dinh Van Huynh, Ngo Si Tung
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FP-Injective and Weakly Quasi-Frobenius Rings
Journal of Mathematical Sciences, 2002 AMSLatex, 15 ...
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