One-variable equational compactness in partially distributive semilattices with pseudocomplementation

Author:

Bulman-Fleming Sydney,Fleischer Isidore

Abstract

A universal algebra A is called one-variable equationally compact if every system of equations with constants in A involving a single variable x, every finite subsystem of which has a solution in A, has itself a solution in A. The one-variable equationally compact semilattices with pseudocomplementation S ; , , 0 \langle S; \wedge {,^ \ast },0\rangle which satisfy the partial distributive law x ( y z ) = ( x y ) ( x z ) x \wedge {(y \wedge z)^ \ast } = (x \wedge {y^ \ast }) \vee (x \wedge {z^ \ast }) are characterized, and as a consequence we are able to describe the one-variable compact Stone semilattices. Similar considerations yield a characterization of the one-variable equationally compact Stone algebras, extending a well known result for distributive lattices.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference22 articles.

1. A representation theory for prime and implicative semilattices;Balbes, Raymond;Trans. Amer. Math. Soc.,1969

2. Stone lattices;Balbes, Raymond;Duke Math. J.,1970

3. A characterization of complete bi-Brouwerian lattices;Beazer, R.;Colloq. Mat.,1974

4. American Mathematical Society Colloquium Publications, Vol. XXV;Birkhoff, Garrett,1967

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