On weak center Galois extensions of rings

George Szeto and Lianyong Xue

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 25, 1-7

Abstract:

Let B be a ring with 1, C the center of B , G a finite automorphism group of B , and B G the set of elements in B fixed under each element in G . Then, the notion of a center Galois extension of B G with Galois group G (i.e., C is a Galois algebra over C G with Galois group G | C ≅ G ) is generalized to a weak center Galois extension with group G , where B is called a weak center Galois extension with group G if B I i = B e i for some idempotent in C and I i = { c − g i ( c ) | c ∈ C } for each g i ≠ 1 in G . It is shown that B is a weak center Galois extension with group G if and only if for each g i ≠ 1 in G there exists an idempotent e i in C and { b k e i ∈ B e i ; c k e i ∈ C e i , k = 1 , 2 , ... , m } such that ∑ k = 1 m b k e i g i ( c k e i ) = δ 1 , g i e i and g i restricted to C ( 1 − e i ) is an identity, and a structure of a weak center Galois extension with group G is also given.

Date: 2001
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/25/239019.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/25/239019.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:239019

DOI: 10.1155/S016117120100504X

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().