On the compatibility of algebraic equations with extensions
Harald Hule, Winfried B. Müller · Journal of the Australian Mathematical Society · 1976
Abstract 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.