Cosets in universal algebra (Q1087898)

Main result (Theorem 1.4): For a variety V the fact that for each \(A\in V\), each \(a\in A\) the natural mapping \(R\mapsto \{x\); \(<x,a>\in R\}\) \(R\in Con A\) is a lattice homomorphism is equivalent to congruence permutability of V. The concept of a so called coset is a generalization of the concept of ideal in universal algebra. Using this concept, the authors give characterizations of congruence permutable regular varieties (Theorem 2.3).