Results 21 to 30 of about 775 (194)
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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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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Canonical Nonclassical Hopf–Galois Module Structure of Nonabelian Galois Extensions [PDF]
Communications in Algebra, 2016 Let $L/K$ be a finite Galois extension of local or global fields in characteristic $0$ or $p$ with nonabelian Galois group $G$, and let ${\mathfrak B}$ be a $G$-stable fractional ideal of $L$. We show that ${\mathfrak B}$ is free over its associated order in $K[G]$ if and only if it is free over its associated order in the Hopf algebra giving the ...
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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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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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Tame Galois module structure revisited [PDF]
Annali di Matematica Pura ed Applicata (1923 -), 2019 16 pages.
Ferri, Fabio, Greither, Cornelius
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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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Equivariant v1,0⃗$v_{1,\vec{0}}$‐self maps
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Let G$G$ be a cyclic p$p$‐group or generalized quaternion group, X∈π0SG$X\in \pi _0 S_G$ be a virtual G$G$‐set, and V$V$ be a fixed point free complex G$G$‐representation. Under conditions depending on the sizes of G$G$, X$X$, and V$V$, we construct a self map v:ΣVC(X)(p)→C(X)(p)$v\colon \Sigma ^V C(X)_{(p)}\rightarrow C(X)_{(p)}$ on the ...
William Balderrama +2 more
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The first two group theory papers of Philip Hall
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this paper, we discuss the first two papers on soluble groups written by Philip Hall and their influence on the study of finite groups. The papers appeared in 1928 and 1937 in the Journal of the London Mathematical Society.
Inna Capdeboscq
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The modular automorphisms of quotient modular curves
Mathematika, Volume 72, Issue 1, January 2026.Abstract We obtain the modular automorphism group of any quotient modular curve of level N$N$, with 4,9∤N$4,9\nmid N$. In particular, we obtain some unexpected automorphisms of order 3 that appear for the quotient modular curves when the Atkin–Lehner involution w25$w_{25}$ belongs to the quotient modular group. We also prove that such automorphisms are
Francesc Bars, Tarun Dalal
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