Filters, Ideals and Congruences on Double Boolean Algebras

Autor:	Tenkeu Jeufack Yannick Léa, Léonard Kwuida, Etienne Romuald Alomo Temgoua
Rok vydání:	2021
Předmět:	Pure mathematics Formal concept analysis Concept algebra Algebra over a field Congruence relation Type (model theory) Algebraic number Equational theory Mathematics
Zdroj:	Formal Concept Analysis ISBN: 9783030778668 ICFCA
DOI:	10.1007/978-3-030-77867-5_18
Popis:	Double Boolean algebras (dBas) are algebras \(\underline{D}:=(D;\sqcap ,\)\(\sqcup ,\lnot ,\lrcorner ,\bot ,\top )\) of type (2, 2, 1, 1, 0, 0), introduced by R. Wille to capture the equational theory of the algebra of protoconcepts. Boolean algebras form a subclass of dBas. Our goal is an algebraic investigation of dBas, based on similar results on Boolean algebras. In these notes, we describe filters, ideals and congruences, and show that principal filters as well as principal ideals of dBas form (non necessary isomorphic) Boolean algebras.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::de965a54ef47bbdbe6671acb80a69557 https://doi.org/10.1007/978-3-030-77867-5_18 Zobrazit plný text záznamu