Congruence relations on De Morgan algebras (Q1121298)

A de Morgan algebra is an algebra (L;\(\vee,\wedge,\sim,0,1)\) of type (2,2,1,0,0) such that (L;\(\vee,\wedge,0,1)\) is a distributive (0,1)- lattice, \(\sim\) is a dual (0,1)-lattice endomorphism (so that \(\sim (a\vee b)=\sim a\wedge \sim b\), \(\sim (a\wedge b)=\sim a\vee \sim b\), \(\sim 0=1\), and \(\sim 1=0)\), and \(\sim \sim a=a)\). In the present paper various classes of de Morgan algebras are investigated whose congruence relations satisfy special conditions together with their interrelationship. In particular, the classes of congruence permutable, congruence regular, and congruence uniform de Morgan algebras are studied.