Subdirectly irreducible semilattices with endomorphism
Pages : 501-508
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Publication Date : 2022-04-01
Article Type : Research
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 ( S ; ∧ , k ) (S;∧,k) in which ( S ; ∧ ) (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