Subdirectly irreducible semilattices with endomorphism

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Hacettepe Journal of Mathematics and Statistics
Volume:51 Issue:2
Subdirectly irreducible semilattices with endomorphism

Subdirectly irreducible semilattices with endomorphism

Authors : Jie FANG

Pages : 501-508

Doi:10.15672/hujms.994459

View : 54 | Download : 12

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

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