On generalized quaternion algebras
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) j2=−1 and jb=σ(b)j for each b in B. The purpose of...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171280000166 |
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| Summary: | 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) j2=−1 and jb=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. |
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| ISSN: | 0161-1712 1687-0425 |