Results 11 to 20 of about 214 (172)
The Galois Theory of Matrix C-rings [PDF]
Applied Categorical Structures, 2006 27 pages ...
Tomasz Brzezinski, Ryan B. Turner
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On Galois Extension of Rings [PDF]
Nagoya Mathematical Journal, 1966 Let Λ be a ring and G a finite group of ring automorphisms of Λ. The totality of elements of Λ which are left invariant by G is a subring of Λ. We call it the G-fixed subring of Λ. Let be the crossed product of Λ and G with trivial factor set, i.e. {u0} is a Λ-free basis of Δ and , and let Γ be a subring of the G-fixed subring of Λ which has the same ...
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A note on a standard model for Galois rings
Applicable Algebra in Engineering, Communication and Computing, 2023 Submitted to ...
Edgar Martínez-Moro +2 more
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On Galois Conditions and Galois Groups of Simple Rings [PDF]
Transactions of the American Mathematical Society, 1965 Throughout the present paper, R will be a simple ring, where we shall understand by a simple ring a total matrix ring over a division rings. If S' is any subring containing the identity element 1 of R, we denote by VR(S') the centralizer of S' in R, VR(S') = VR(VR(S')) and by 0 (S', R) we denote the group of all automorphisms of R which are the ...
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Galois actions on rings and finite Galois coverings.
MATHEMATICA SCANDINAVICA, 1989 This paper is devoted to developing a general finite Galois theory for rings which when specialized to finite dimensional algebras over an algebraically closed field gives the Bongartz, Gabriel and Riedtmann theory of finite Galois coverings and when specialized to commutative rings gives the usual Galois theory of commutative rings.
Auslander, M., Reiten, I., Smalo, S.O.
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On a notion of “Galois closure” for extensions of rings [PDF]
Journal of the European Mathematical Society, 2014 We introduce a notion of “Galois closure” for extensions of rings. We show that the notion agrees with the usual notion of Galois closure in the case of an S_n degree n
Bhargava, Manjul, Satriano, Matthew
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An Authentication Code over Galois Rings with Optimal Impersonation and Substitution Probabilities
Mathematical and Computational Applications, 2018 Two new systematic authentication codes based on the Gray map over a Galois ring are introduced. The first introduced code attains optimal impersonation and substitution probabilities.
Juan Carlos Ku-Cauich +2 more
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SERRE WEIGHTS AND BREUIL’S LATTICE CONJECTURE IN DIMENSION THREE
Forum of Mathematics, Pi, 2020 We prove in generic situations that the lattice in a tame type induced by the completed cohomology of a $U(3)$-arithmetic manifold is purely local, that is, only depends on the Galois representation at places above $p$. This is a generalization to $\text{
DANIEL LE +3 more
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Normal Bases on Galois Ring Extensions [PDF]
Symmetry, 2018 In this paper we study the normal bases for Galois ring extension ${{R}} / {Z}_{p^r}$ where ${R}$ = ${GR}$(pr, n). We present a criterion on normal basis for ${{R}} / {Z}_{p^r}$ and reduce this problem to one of finite field extension $\overline{R} / \overline{Z}_{p^r}=F_{q} / F_{p} (q=p^n)$ by Theorem 1. We determine all optimal normal bases
Zhang Aixian, Feng Keqin
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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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