Bożena Piekart, Andrzej Walendziak, “On filters and upper sets in CI-algebras”, Algebra Discrete Math., 2011, Volume 11, Issue 1,Pages <nobr>109

This article is cited in 4 papers

RESEARCH ARTICLE

On filters and upper sets in CI-algebras

Bożena Piekart^a, Andrzej Walendziak^b

^a Institute of Mathematics and Physics, University of Siedlce, 3 Maja 54, 08–110 Siedlce, Poland
^b Warsaw School of Information Technology, Newelska 6, 01–447 Warszawa, Poland

Abstract: CI-algebras are a generalization of BE-algebras and dual BCK/BCI/BCH-algebras. In this paper filters of CI-algebras are considered. Given a subset of a CI-algebra, the least filter containing it is constructed. An equivalent condition of the filters using the notion of upper sets is provided.

Keywords: CI-algebra, filter, upper set.

MSC: 06F35, 03G25

Received: 24.07.2010
Revised: 18.03.2011

Language: English