International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1982 / Article

Open Access

Volume 5 |Article ID 260102 | 6 pages | https://doi.org/10.1155/S0161171282000714

On separable abelian extensions of rings

Received09 Feb 1982

Abstract

Let R be a ring with 1, G(=ρ1××ρm) a finite abelian automorphism group of R of order n where ρi is cyclic of order ni. for some integers n, ni, and m, and C the center of R whose automorphism group induced by G is isomorphic with G. Then an abelian extension R[x1,,xm] is defined as a generalization of cyclic extensions of rings, and R[x1,,xm] is an Azumaya algebra over K(=CG={cinC/(c)ρi=cfor eachρiinG}) such that R[x1,,xm]RGKC[x1,,xm] if and only if C is Galois over K with Galois group G (the Kanzaki hypothesis).

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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