Results 11 to 20 of about 1,341,218 (213)
The Extension Theorem for Bi-invariant Weights over Frobenius Rings and Frobenius Bimodules [PDF]
Contemporary Mathematics, 2017 We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobenius ring as a special case.
O. W. Gnilke +4 more
semanticscholar +3 more sources
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.
Zhu, Zhanmin
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Rings of Frobenius operators [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2014 AbstractLet R be a local ring of prime characteristic. We study the ring of Frobenius operators ${\mathcal F}(E)$, where E is the injective hull of the residue field of R. In particular, we examine the finite generation of ${\mathcal F}(E)$ over its degree zero component ${\mathcal F}^0(E)$, and show that ${\mathcal F}(E)$ need not be finitely ...
Katzman, Mordechai +3 more
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On Almost Quasi-Frobenius Fuzzy Rings [PDF]
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
doaj +2 more sources
Matrix product codes over finite commutative Frobenius rings [PDF]
Designs, Codes and Cryptography, 2012 Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes constructed with several types of matrices is bounded in different ways.
Yun Fan, S. Ling, Hongwei Liu
semanticscholar +3 more sources
On the construction of quasi-Frobenius rings [PDF]
Journal of Algebra, 1973 AbstractA quasi-Frobenius ring (QF ring) is a left Artinian ring R with identity for which the left R-module RR is injective. Since Nakayama [8] introduced the notion of a QF ring, quasi-Frobenius rings have been extensively studied. It is well known that for any QF ring R, both Rn, the ring of n × n matrices over R, and RG, group ring over R for any ...
Hannula, T.A
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Self-dual codes over commutative Frobenius rings [PDF]
Finite Fields Their Appl., 2010 We prove that self-dual codes exist over all finite commutative Frobenius rings, via their decomposition by the Chinese Remainder Theorem into local rings.
S. Dougherty +3 more
semanticscholar +3 more sources
Do non-free LCD codes over finite commutative Frobenius rings exist? [PDF]
Designs, Codes and Cryptography, 2019 In this paper, we clarify some aspects of LCD codes in the literature. We first prove that non-free LCD codes do not exist over finite commutative Frobenius local rings.
S. Bhowmick +4 more
semanticscholar +1 more source
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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DNA codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2022 A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 5 and nilpotency index 4, and k-tuples of DNA codewords is established.
Castillo-Guillén C. A. +1 more
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