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Relations between the amalgamation property and algebraic equations

Published online by Cambridge University Press:  09 April 2009

Harald Hule
Harald Hule
Affiliation:
Departamento de Matemática, Universidade de Brasília, Brazil.
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Abstract

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A variety B is called solutionally complete if any system of algebraic equations over an algebra A in B has a solution in A provided it is solvable in B and has at most one solution in any extension of A in B. B is called solutionally compatible if every solvable system of equations over an algebra in B is also solvable over any extension of that algebra. It is shown that solutional compatibility is equivalent with the amalgamation property and that a weaker form of the strong amalgamation property is sufficient but not necessary for equational completeness.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 3 , May 1978 , pp. 257 - 263
Copyright
Copyright © Australian Mathematical Society 1978

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