Subdirectly irreducible semilattices with endomorphism
Pages : 501-508
View : 19 | Download : 7
Publication Date : 2022-04-01
Article Type : Research Paper
Abstract :In this paper we initiate an investigation into the class of meet semilattices endowed with an endomorphism. A consideration of the subdirectly irreducible algebras leads to a description of a subclass of those algebras insert ignore into journalissuearticles values( S ; ∧ , k ); insert ignore into journalissuearticles values(S;∧,k); in which insert ignore into journalissuearticles values( S ; ∧ ); insert ignore into journalissuearticles values(S;∧); is a meet semilattice and k k is an endomorphism on S S characterised by the property k ⩾ i d S k⩾idS . We particularly show that such an algebra is subdirectly irreducible if and only if it is a chain with one of the following forms ⋯ < a j < a j − 1 < ⋯ < a 0 ⋯
Keywords : Semilattice, endomorphism, subdirectly irreducible
