A groupoid characterization of Boolean algebras

• Autorzy: Ivan Chajda
• Języki publikacji: EN

Abstrakty

EN

We present a groupoid which can be converted into a Boolean algebra with respect to term operations. Also conversely, every Boolean algebra can be reached in this way.

Słowa kluczowe

EN

groupoid; Boolean algebra; semi-bolean algebra; involution; dualautomorphism (or antiautomorphism)

Kategorie tematyczne

• 20N02: Sets with a single binary operation (groupoids)
• 06F99: None of the above, but in this section
• 08C10: Axiomatic model classes
• 03G25: Other algebras related to logic
• 06A11: Algebraic aspects of posets
• 03G05: Boolean algebras

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2004
• Tom: 24
• Numer: 2
• Strony: 177-184

Daty

wydano

2004

otrzymano

2003-12-23

poprawiono

2004-12-29

Twórcy

autor

Ivan Chajda

• Department of Algebra and Geometry, Palacký University of Olomouc, Tomkova 40; 779 00 Olomouc, Czech Republic

Bibliografia

• [1] J.C. Abbott, Semi-boolean algebra, Mat. Vestnik 4 (1967), 177-198.
• [2] G. Birkhoff, Lattice Theory, third edition, Publ. Amer. Math. Soc., Providence, RI, 1967.
• [3] J. Dudek, Polynomials in idempotent commutative groupoids, Dissert. Math. 286 (1989), 1-59.

Identyfikatory

DOI

10.7151/dmgaa.1083