On separable abelian extensions of rings

George Szeto

International Journal of Mathematics and Mathematical Sciences, 1982, vol. 5, 1-6

Abstract:

Let R be a ring with 1 , G ( = 〈 ρ 1 〉 × … × 〈 ρ m 〉 ) a finite abelian automorphism group of R of order n where 〈 ρ i 〉 is cyclic of order n i . for some integers n , n i , and m , and C the center of R whose automorphism group induced by G is isomorphic with G . Then an abelian extension R [ x 1 , … , x m ] is defined as a generalization of cyclic extensions of rings, and R [ x 1 , … , x m ] is an Azumaya algebra over K ( = C G = { c in C / ( c ) ρ i = c for each ρ i in G } ) such that R [ x 1 , … , x m ] ≅ R G ⊗ K C [ x 1 , … , x m ] if and only if C is Galois over K with Galois group G (the Kanzaki hypothesis).

Date: 1982
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/5/260102.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/5/260102.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:260102

DOI: 10.1155/S0161171282000714

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 ().