| Autor: |
Szeto, George, Xue, Lianyong |
| Předmět: |
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| Zdroj: |
Communications in Algebra; Dec2007, Vol. 35 Issue 12, p3979-3985, 7p |
| Abstrakt: |
Let B be a Galois algebra over a commutative ring R with Galois group G such that BH is a separable subalgebra of B for each subgroup H of G. Then it is shown that B satisfies the fundamental theorem if and only if B is one of the following three types: (1) B is an indecomposable commutative Galois algebra, (2) B = Re ⊕ R(1 - e) where e and 1 - e are minimal central idempotents in B, and (3) B is an indecomposable Galois algebra such that for each separable subalgebra A, VB(A) = ⊕∑g∈G(A)Jg, and the centers of A and BG(A) are the same where VB(A) is the commutator subring of A in B, Jg = {b ∈ B | bx = g(x)b for each x ∈ B} for a g ∈ G, and G(A) = {g ∈ G | g(a) = a for all a ∈ A}. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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