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Solutionally complete varieties

Published online by Cambridge University Press:  09 April 2009

Harald Hule
Harald Hule
Affiliation:
Departamento de Matemática Universidade de BrasíliaBrasilia, Brazil
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Abstract

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A veristy is called solutionally complete if any solvable system of algebraic equations over an algebra A in which has at most one solution in every extension of A in has the solution in A. A necessary and sufficient condition for solutional completeness is given which is a weaker form of the strong amalgamation property.

Subject classification (Amer. Math. Soc. (MOS) 1970): 08 A 15.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1979 , pp. 82 - 86
Copyright
Copyright © Australian Mathematical Society 1979

References

Hule, H. (1976), ‘Über die Eindeutigkeit der Lösungen algebraischer Gleichungssysteme’ J. Reine Angew. Math. 282, 157–161.Google Scholar
Hule, H. (1978), ‘Relations between the amalgamation property and algebraic equations’ J. Austral. Math. Soc. Ser. A 25, 257–263.CrossRefGoogle Scholar
Lausch, H. and Nöbauer, W. (1973), Algebra of polynomials (North-Holland, Amsterdam).Google Scholar
Taylor, W. (1976), ‘Pure compactifications in quasi-primal varieties’, Canad. J. Math. 28, 50–62.CrossRefGoogle Scholar