Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



One-variable equational compactness in partially distributive semilattices with pseudocomplementation

Authors: Sydney Bulman-Fleming and Isidore Fleischer
Journal: Proc. Amer. Math. Soc. 79 (1980), 505-511
MSC: Primary 06A12; Secondary 08A45
MathSciNet review: 572290
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $ \langle S; \wedge {,^ \ast },0\rangle $ which satisfy the partial distributive law $ 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06A12, 08A45

Retrieve articles in all journals with MSC: 06A12, 08A45

Additional Information

Keywords: Semilattice, pseudocomplement, equationally compact
Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society