Results 21 to 30 of about 48,689 (198)
GALOIS AUTOMORPHISMS AND CLASSICAL GROUPS
Transformation Groups, 2022 v1. 40 pages; v2. 42 pages. Corrected the statement of Thm. C and updated Section 16 to reflect this change. No other changes; v3.
Taylor, Jay; id_orcid 0000-0002-9143-6605 +1 more
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On characterizations of a center Galois extension
International Journal of Mathematics and Mathematical Sciences, 2000 Let B be a ring with 1, C the center of B, G a finite automorphism group of B, and BG the set of elements in B fixed under each element in G. Then, it is shown that B is a center Galois extension of BG (that is, C is a Galois algebra over CG with ...
George Szeto, Lianyong Xue
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Journal of Algebra, 1999 Let \(f(X)= X^n+ aX^s+b\) be an irreducible trinomial with integral coefficients, where \(n\) and \(s\) are co-prime. Under which criteria on the coefficients \(a,b\), the Galois group of \(f(X)\) must be the symmetric group \(S_n\)? Examples of such criteria have been given by \textit{H. Osada} [J.
Cohen, S.D, Movahhedi, A, Salinier, A
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The Boolean algebra of Galois algebras
International Journal of Mathematics and Mathematical Sciences, 2003 Let B be a Galois algebra with Galois group G, Jg={b∈B|bx=g(x)b for all x∈B} for each g∈G, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero element in Ba, and He={g∈G|eeg=e}.
George Szeto, Lianyong Xue
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Approximating absolute Galois groups [PDF]
Journal of Pure and Applied Algebra, 2022 13 pages.
Carlsson, Gunnar, Joshua, Roy
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The Galois extensions induced by idempotents in a Galois algebra
International Journal of Mathematics and Mathematical Sciences, 2002 Let B be a Galois algebra with Galois group G, Jg={b∈B|bx=g(x)b for all x∈B} for each g∈G, eg the central idempotent such that BJg=Beg, and eK=∑g∈K,eg≠1eg for a subgroup K of G.
George Szeto, Lianyong Xue
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On Galois projective group rings
International Journal of Mathematics and Mathematical Sciences, 1991 Let A be a ring with 1, C the center of A and G′ an inner automorphism group of A induced by {Uα in A/α in a finite group G whose order is invertible}.
George Szeto, Linjun Ma
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The Boolean algebra and central Galois algebras
International Journal of Mathematics and Mathematical Sciences, 2001 Let B be a Galois algebra with Galois group G, Jg={b∈B∣bx=g(x)b for all x∈B} for g∈G, and BJg=Beg for a central idempotent eg. Then a relation is given between the set of elements in the Boolean algebra (Ba,≤) generated by {0,eg∣g∈G} and a set of ...
George Szeto, Lianyong Xue
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Skew group rings which are Galois
International Journal of Mathematics and Mathematical Sciences, 2000 Let S*G be a skew group ring of a finite group G over a ring S. It is shown that if S*G is an G′-Galois extension of (S*G)G′, where G′ is the inner automorphism group of S*G induced by the elements in G, then S is a G-Galois extension of SG.
George Szeto, Lianyong Xue
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