Abstract
This chapter discusses epimorphisms in discriminator varieties. Epimorphism are onto maps in certain discriminator varieties. It presents a theorem in which V is a discriminator variety such that the class Vs of all simple members of V has the amalgamation property (AP) and the property (ES) that all epimorphisms are onto maps. Then, V satisfies ES. Strong amalgamation property (SAP) holds in every discriminator variety V for which Vs has AP and ES. An algebra ▪ is called homogeneous if each proper inner automorphism of ▪ extends to an automorphism of ▪. A residually finite variety V generated by finitely many independent demi-primal algebras has ES and SAP. A variety generated by a demi-primal algebra has ES and SAP.
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