Discussiones Mathematicae General Algebra and Applications 24(2) (2004) 177-184
doi: 10.7151/dmgaa.1083

[BIBTex] [PDF] [PS]

A GROUPOID CHARACTERIZATION OF BOOLEAN ALGEBRAS

Ivan Chajda

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

e-mail:chajda@inf.upol.cz

Abstract

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.

Keywords: groupoid, Boolean algebra, semi-bolean algebra, involution, dualautomorphism (or antiautomorphism).

2000 Mathematics Subject Classification: 20N02, 03G05 03G25, 06A11, 06F99, 08C10.

References

[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.

Received 23 December 2003
Revised 29 December 2004