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On the compatibility of algebraic equations with extensions

Published online by Cambridge University Press:  09 April 2009

Harald Hule  and
Winfried B. Müller
Harald Hule
Affiliation:
Departmento de Matemático, Universidade de Brasilia, 70,000 Brasilia, D.F., Brazil.
Winfried B. Müller
Affiliation:
Institut für Mathematik I Universität für Bildungswissenschaften, A-9010 Klagenfurt, Australia.
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Abstract

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In this paper we investigate the following problem proposed by Lausch and Nöbauer: Let be a variety of universal algebras, B an algebra of and A a subalgebra of B. If a system of algebraic equations over A is solvable in , is it then solvable over B? We show that the answer is affirmative in certain varieties but negative in the general case.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 3 , May 1976 , pp. 381 - 383
Copyright
Copyright © Australian Mathematical Society 1976

References

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Lausch, H. and Nöbauer, W. (1973), Algebra of Polynomials (North Holland, Amsterdam, 1973).Google Scholar