Results 1 to 10 of about 222 (113)
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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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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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established ...
Castillo-Guillén C. A. +1 more
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Constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 The family of finite local Frobenius non-chain rings of length 5 and nilpotency index 4 is determined, as a by-product all finite local Frobenius non-chain rings with p5 elements (p a prime) and nilpotency index 4 are given.
Castillo-Guillén C. A. +1 more
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Noise Free Fully Homomorphic Encryption Scheme Over Non-Associative Algebra
IEEE Access, 2020 Among several approaches to privacy-preserving cryptographic schemes, we have concentrated on noise-free homomorphic encryption. It is a symmetric key encryption that supports homomorphic operations on encrypted data.
Iqra Mustafa +6 more
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Frobenius and valuation rings [PDF]
Algebra & Number Theory, 2016 The behavior of the Frobenius map is investigated for valuation rings of prime characteristic. We show that valuation rings are always F-pure. We introduce a generalization of the notion of strong F-regularity, which we call F-pure regularity, and show that a valuation ring is F-pure regular if and only if it is Noetherian.
Datta, Rankeya, Smith, Karen
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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
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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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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