On the variety generated by positive reducts of Tarski's relation algebras
by
D.A. Bredikhin
Saratov State Technical University

Tarski's relation algebra (RA) is an algebra of the form (A, ·, ^-1, e, \/ , /\ , ^-), where (A, \/ , /\ , ^-) is a Boolean algebra, (A, ·, ^-1, e) is an involuted monoid, · and ^-1 distribute over \/ , and the following equation holds: x^-1(xy)^- <= y^-. For any RA (A, ·, ^-1, e, \/ , /\ , ^-), an algebra (A, ·, ^-1, e, \/ , /\ ) is called a positive reduct of RA. Let V be the variety generated by the class of all positive reducts of RA.

THEOREM. An algebra (A, ·, ^-1, e, \/ , /\ ) belongs to V if and only if (A, \/ , /\ ) is a distributive lattice, (A, ·, ^-1, e) is an involuted monoid, · and ^-1 distribute over \/ , and the following equation holds: x /\ yz=x /\ y(z /\ x^-1y).

Date received: November 2, 2000