Results 1 to 10 of about 3,053 (239)
On weak center Galois extensions of rings
International Journal of Mathematics and Mathematical Sciences, 2001 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, the notion of a center Galois extension of BG with Galois group G (i.e., C is a Galois algebra over CG ...
George Szeto, Lianyong Xue
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On the Galois group of three classes of trinomials
AIMS Mathematics, 2022 Let $ n\ge 8 $ be an integer and let $ p $ be a prime number satisfying $ \frac{n}{2} < p < n-2 $. In this paper, we prove that the Galois groups of the trinomials $ T_{n, p, k}(x): = x^n+n^kp^{(n-1-p)k}x^p+n^kp^{nk}, $ $ S_{n, p}(x): =
Lingfeng Ao +2 more
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On central commutator Galois extensions of rings
International Journal of Mathematics and Mathematical Sciences, 2000 Let B be a ring with 1, G a finite automorphism group of B of order n for some integer n, BG the set of elements in B fixed under each element in G, and Δ=VB(BG) the commutator subring of BG in B.
George Szeto, Lianyong Xue
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Rationally connected rational double covers of primitive Fano varieties [PDF]
Épijournal de Géométrie Algébrique, 2020 We show that for a Zariski general hypersurface $V$ of degree $M+1$ in ${\mathbb P}^{M+1}$ for $M\geqslant 5$ there are no Galois rational covers $X\dashrightarrow V$ of degree $d\geqslant 2$ with an abelian Galois group, where $X$ is a rationally ...
Aleksandr V. Pukhlikov
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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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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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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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