On filters and upper sets in CI-algebras

• Date: 2018
• Main Authors: Piekart, Bozena, Walendziak, Andrzej
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: CI-algebra; filter; upper set; 06F35; 03G25
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/662
• Journal Title: Algebra and Discrete Mathematics

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.