Some remarks on distributive semilattices

Sergio A. Celani; Ismael Calomino

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Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices

Sergio A. Celani (2015)

Open Mathematics

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In this paper we shall study a notion of relative annihilator-preserving congruence relation and relative annihilator-preserving homomorphism in the class of bounded distributive semilattices. We shall give a topological characterization of this class of semilattice homomorphisms. We shall prove that the semilattice congruences that are associated with filters are exactly the relative annihilator-preserving congruence relations.

Some remarks on certain classes of semilattices.

Murty, P.V.Ramana, Murty, M.Krishna (1982)

International Journal of Mathematics and Mathematical Sciences

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Quasicomplemented semilattices

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Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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On distributive trices

Kiyomitsu Horiuchi, Andreja Tepavčević (2001)

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A triple-semilattice is an algebra with three binary operations, which is a semilattice in respect of each of them. A trice is a triple-semilattice, satisfying so called roundabout absorption laws. In this paper we investigate distributive trices. We prove that the only subdirectly irreducible distributive trices are the trivial one and a two element one. We also discuss finitely generated free distributive trices and prove that a free distributive trice with two generators has 18 elements. ...

Subdirectly irreducible sectionally pseudocomplemented semilattices

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Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented...

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