International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 7, Pages 489-495
On weak center Galois extensions of rings
Mathematics Department, Bradley University, Peoria 61625, IL, USA
Received 27 April 2000
Copyright © 2001 George Szeto and Lianyong Xue. 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.
Let be a ring with 1, the center of , a finite automorphism group of , and the set of elements in fixed under each element in . Then, the notion of a center
Galois extension of with Galois group (i.e., is a Galois algebra over with Galois group ) is generalized to a weak center Galois extension with group , where is called a weak center Galois extension with group if for some idempotent in and for each in . It is shown that is a weak center Galois extension with group if and only if for each in there exists an idempotent in and such that and restricted to is an identity, and a structure of a weak center Galois extension with group is also given.