Relations between the amalgamation property and algebraic equations

Harald Hule
1978 Journal of the Australian Mathematical Society  
A variety 93 is called solutionally complete if any system of algebraic equations over an algebra A in 93 has a solution in A provided it is solvable in 93 and has at most one solution in any extension of A in 93. 93 is called solutionally compatible if every solvable system of equations over an algebra in 93 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
more » ... strong amalgamation property is sufficient but not necessary for equational completeness. 257
doi:10.1017/s1446788700021005 fatcat:ehsi36glyzel5nn3tzdtb5gr7e