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)



Pseudo-complements in posets

Author: P. V. Venkatanarasimhan
Journal: Proc. Amer. Math. Soc. 28 (1971), 9-17
MSC: Primary 06.35
MathSciNet review: 0272687
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a theory of pseudo-complements is developed for posets (partially ordered sets). The concepts of ideal and semi-ideal are introduced for posets and a few results about them are obtained. These results together with known results about pseudo-complements in distributive lattices lead to the main results. It is proved that if in a pseudo-complemented semilattice or dual semilattice every element is normal, then it is a Boolean algebra. Using this result new proofs for two known theorems are obtained. The existence of maximal ideals in posets is established and it is shown that the dual ideal of dense elements of a poset with 0 is the product of all the maximal dual ideals.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06.35

Retrieve articles in all journals with MSC: 06.35

Additional Information

Keywords: Poset, lattice, semilattice, Boolean algebra, ideal, semiideal, complement, relative-complement, pseudo-complement, quasi-complement, normal element, dense element
Article copyright: © Copyright 1971 American Mathematical Society