DISTRIBUTIVE LATTICES WITH A HOMOMORPHIC OPERATION
Cong-wen Luo, Gao-xia Wang · 2018
In this paper, we initiate an investigation into the class eD of extended bounded distributive lattices, namely, bounded distributive lattices endowed with an unary operation, which is an endomorphism. By using the set of fixed points and congruences, we characterise the (finitely) subdirectly irreducible algebras in ep, qD. In particular, we show that for every algebra in ep, qD, the properties of being finitely subdirectly irreducible and subdirectly irreducible are equivalent. Some results obtained by Balbes and Dwinger on semilattices, distributive lattices and Boolean algebras are generalized.