On generalized quaternion algebras

George Szeto

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-9

Abstract:

Let B be a commutative ring with 1 , and G ( = { σ } ) an automorphism group of B of order 2 . The generalized quaternion ring extension B [ j ] over B is defined by S . Parimala and R . Sridharan such that (1) B [ j ] is a free B -module with a basis { 1 , j } , and (2) j 2 = − 1 and j b = σ ( b ) j for each b in B . The purpose of this paper is to study the separability of B [ j ] . The separable extension of B [ j ] over B is characterized in terms of the trace ( = 1 + σ ) of B over the subring of fixed elements under σ . Also, the characterization of a Galois extension of a commutative ring given by Parimala and Sridharan is improved.

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:728963

DOI: 10.1155/S0161171280000166

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