Congruently local V-groupoids with identity form a variety
Let V be a variety of algebras of type \(\tau\) having no nullary operations. The class l(V) of congruently local V-algebras is defined to consist of those algebras of type \(\tau\) which have a congruence R such that each class of R is a subalgebra contained in V. The main result of this paper is the following: Theorem. Suppose that a variety V has a binary term t and a constant unary term e being a neutral element for t, that is, V satisfies: i) \(e(x)=e(y)\), ii) \(t(x,e(y))=t(e(y),x)=x.\) Then l(V) is a variety.
scientific article; zbMATH DE number 4204419