Generalizations of the primitive element theorem
In this paper we generalize the primitive element theorem to the generation of separable algebras over fields and rings. We prove that any finitely generated separable algebra over an infinite field is generated by two elements and if the algebra is commutative it can be generated by one element. We...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000637 |
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| Summary: | In this paper we generalize the primitive element theorem to the
generation of separable algebras over fields and rings. We prove that any
finitely generated separable algebra over an infinite field is generated by
two elements and if the algebra is commutative it can be generated by one
element. We then derive similar results for finitely generated separable
algebras over semilocal rings. |
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| ISSN: | 0161-1712 1687-0425 |