Results 11 to 20 of about 772 (199)
Gorenstein Flat Modules of Hopf-Galois Extensions
Mathematics, 2023 Let A/B be a right H-Galois extension over a semisimple Hopf algebra H. The purpose of this paper is to give the relationship of Gorenstein flat dimensions between the algebra A and its subalgebra B, and obtain that the global Gorenstein flat dimension ...
Qiaoling Guo +3 more
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Journal of Mathematics, 2022 Let R0=GRpkr,pk be a Galois maximal subring of R so that R=R0⊕U⊕V⊕W⊕Y, where U,V,W, and Y are R0/pR0 spaces considered as R0-modules, generated by the sets u1,⋯,ue,v1,⋯,vf,w1,⋯,wg, and y1,⋯,yh, respectively.
Hezron Saka Were, Maurice Owino Oduor
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A block encryption algorithm based on exponentiation transform
Cogent Engineering, 2020 This paper proposes a new block encryption algorithm for cryptographic information protection. It describes a new transformation method EM (Exponentiation Module), which is part of the algorithm, and a method of S-box obtaining.
Nursulu Kapalova +3 more
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Invariance of recurrence sequences under a galois group
International Journal of Mathematics and Mathematical Sciences, 1996 Let F be a Galois field of order q, k a fixed positive integer and R=Fk×k[D] where D is an indeterminate. Let L be a field extension of F of degree k. We identify Lf with fk×1 via a fixed normal basis B of L over F. The F-vector space Γk(F)(=Γ(L)) of all
Hassan Al-Zaid, Surjeet Singh
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Self-Dual Normal Basis of a Galois Ring
Journal of Mathematics, 2014 Let R′=GR(ps,psml) and R=GR(ps,psm) be two Galois rings. In this paper, we show how to construct normal basis in the extension of Galois rings, and we also define weakly self-dual normal basis and self-dual normal basis for R′ over R, where R′ is ...
Irwansyah +3 more
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Integral Galois module structure for elementary abelian extensions with a Galois scaffold [PDF]
Proceedings of the American Mathematical Society, 2014 This paper justifies an assertion in (Elder, Proc AMS 137 (2009), no 4, 1193--1203) that Galois scaffolds make the questions of Galois module structure tractable. Let $k$ be a perfect field of characteristic $p$ and let $K=k((T))$. For the class of characteristic $p$ elementary abelian $p$-extensions $L/K$ with Galois scaffolds described in mentioned ...
Byott, Nigel P., Elder, G. Griffith
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On generalized quaternion algebras
International Journal of Mathematics and Mathematical Sciences, 1980 Let B be a commutative ring with 1, and G(={σ}) an automorphism group of B of order 2. The generalized quaternion ring extension B[j] over B is defined by S. Parimala and R.
George Szeto
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Hopf-Galois module structure of quartic Galois extensions of $\mathbb{Q}$
, 2021 Given a quartic Galois extension $L/\mathbb{Q}$ of number fields and a Hopf-Galois structure $H$ on $L/\mathbb{Q}$, we study the freeness of the ring of integers $\mathcal{O}_L$ as module over the associated order $\mathfrak{A}_H$ in $H$. For the classical Galois structure $H_c$, we know by Leopoldt's theorem that $\mathcal{O}_L$ is $\mathfrak{A}_{H_c}$
Gil-Muñoz, Daniel, Rio, Anna
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Carlitz Modules and Galois Module Structure
Journal of Number Theory, 1997 Let \(N\) be a finite abelian extension of the function field \(K= \mathbb F_q (T)\) with Galois group \(\Gamma\) and \(O_N\) the integral closure of \(O_K= \mathbb F_q [T]\) in \(N\). Supposing that no prime ideal of \(O_N\) is wildly ramified in \(N\), \textit{R. J. Chapman} [J. Lond. Math. Soc., II. Ser.
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Galois representations of Iwasawa modules [PDF]
Acta Arithmetica, 1986 Let \(p\) be an odd prime. The composite of a finite extension of \(\mathbb Q\) with the unique \(\mathbb Z_p\)-extension over \(\mathbb Q\) is called a \(\mathbb Z_p\)-field. Let \(L/K\) be a finite Galois \(p\)-extension of \(\mathbb Z_p\)-fields of CM-type. Let \(G=\text{Gal}(L/K)\) and \(A^-_ K\) (resp.
Gold, Robert, Madan, Manohar
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