Modular elements in congruence lattices of \(G\)-sets
Let \(A\) be a nonvoid set and \(\varphi\) a homomorphism from a group \(G\) into the full transformation group of \(A\). Then \(A\) with the set of unary operations \(g(a)= (\varphi(g))(a)\), \(a\in A\), \(g\in G\), on \(A\) is called a \(G\)-set. An element \(x\) in a lattice \(L\) is called modular if \((x\vee y)\wedge z= (x\wedge z)\vee y\) for \(y,z\in L\), \(y\leq z\). The aim of the paper is to describe modular elements in congruence lattices of \(G\)-sets.
scientific article; zbMATH DE number 1428663