Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
semilat\/tice; lat\/tice; antitone involution; congruence permutability; weak regularity
semilat\/tice; lat\/tice; antitone involution; congruence permutability; weak regularity
Summary:
We study $\vee$-semilat\/tices and lat\/tices with the greatest element 1 where every interval [p,1] is a lat\/tice with an antitone involution. We characterize these semilat\/tices by means of an induced binary operation, the so called sectionally antitone involution. This characterization is done by means of identities, thus the classes of these semilat\/tices or lat\/tices form varieties. The congruence properties of these varieties are investigated.
References:
[1] Abbott J.C.: Semi-boolean algebras. Matem. Vestnik 4 (1967), 177-198. MR 0239957
[2] Burris S., Sankappanavar H.P.: A Course in Universal Algebra. Springer-Verlag, 1981. MR 0648287 | Zbl 0478.08001
[3] Chajda I.: An extension of relative pseudocomplementation to non-distributive lattices. Acta Sci. Math. (Szeged), to appear. MR 2034188 | Zbl 1048.06005
[4] Chajda I., Halaš R., Länger H.: Orthomodular implication algebras. Internat. J. Theoret. Phys. 40 (2001), 1875-1884. MR 1860644 | Zbl 0992.06008
[5] Csakany B.: Characterizations of regular varieties. Acta Sci. Math. (Szeged) 31 (1970), 187-189. MR 0272697 | Zbl 0216.03302
[6] Werner H.: A Mal'cev condition on admissible relations. Algebra Universalis 3 (1973), 263. MR 0330009
Search
Partner of
