On filters and upper sets in CI-algebras

• Veröffentlicht in: Algebra and Discrete Mathematics
• Datum: 2011
• Hauptverfasser: Piekart, B., Walendziak, A.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2011
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/154765
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: On filters and upper sets in CI-algebras / B. Piekart, A. Walendziak // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 1. — С. 109–115. — Бібліогр.: 13 назв. — англ.

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.