On separable cyclic extensions of rings

George Szeto; Yuen-Fat Wong

doi:10.1017/s1446788700024514

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On separable cyclic extensions of rings

George Szeto Yuen-Fat Wong

Year: 1982 Journal: Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics Vol: 32 (2)Pages: 165-170 Publisher: Cambridge University Press

DOI: 10.1017/s1446788700024514

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Abstract

Abstract The quaternion algebra of degree 2 over a commutative ring as defined by S. Parimala and R. Sridharan is generalized to a separable cyclic extension B [ j ] of degree n over a noncommutative ring B . A characterization of such an extension is given, and a relation between Azumaya algebras and Galois extensions for B [ j ] is also obtained.

Keywords:

Mathematics Noncommutative geometry Separable space Noncommutative ring Ring (chemistry) Pure mathematics Extension (predicate logic) Quaternion Characterization (materials science) Commutative ring Galois extension Algebra over a field Degree (music) Commutative property Galois group Discrete mathematics Mathematical analysis

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Topics

Algebraic structures and combinatorial models

Physical Sciences → Mathematics → Geometry and Topology

Rings, Modules, and Algebras

Physical Sciences → Mathematics → Algebra and Number Theory

Commutative Algebra and Its Applications

Physical Sciences → Mathematics → Algebra and Number Theory

On separable cyclic extensions of rings

Abstract

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