Subdirectly Irreducible and Semisimple Double Boolean Algebras

Kwuida, Léonard; Temgoua Alomo, Etienne Romuald (2024). Subdirectly Irreducible and Semisimple Double Boolean Algebras In: Cabrera, Inma P.; Ferré, Sébastien; Obiedkov, Sergei (eds.) Conceptual Knowledge Structures: First International Joint Conference, CONCEPTS 2024, Cádiz, Spain, September 9–13, 2024, Proceedings. Lecture Notes in Computer Science: Vol. 14914 (pp. 3-19). Cham: Springer Nature 10.1007/978-3-031-67868-4_1

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Double Boolean algebras are algebras of type (2, 2, 1, 1, 0, 0) introduced by Rudolf Wille to capture the equational theory of protoconcept algebras. A famous theorem of Birkhoff says that any variety is determined by its subdirectly irreducible members. In this work we give a construction that leads to a concrete embedding of double Boolean algebras into the protoconcept algebra. We characterize subdirectly irreducible, simple and semisimple double Boolean algebras.

Item Type:	Book Section (Book Chapter)
Division/Institute:	Business School > Institute for Applied Data Science & Finance Business School > Institute for Applied Data Science & Finance > Applied Data Science Business School
Name:	Kwuida, Léonard0000-0002-9811-0747; Temgoua Alomo, Etienne Romuald; Cabrera, Inma P.; Ferré, Sébastien and Obiedkov, Sergei
ISSN:	1611-3349
ISBN:	978-3-031-67867-7
Series:	Lecture Notes in Computer Science
Publisher:	Springer Nature
Language:	English
Submitter:	Léonard Kwuida
Date Deposited:	21 Aug 2024 10:45
Last Modified:	21 Aug 2024 10:45
Publisher DOI:	10.1007/978-3-031-67868-4_1
URI:	https://arbor.bfh.ch/id/eprint/22208