Principal congruences on semi-De Morgan algebras (Q5939998)

A semi-De Morgan algebra is an algebra \((L,\wedge, \vee, { }',0,1)\) of type \((2,2,1,0,0)\) such that \((L,\wedge,\vee,0,\) \(1)\) is a bounded distributive lattice and the following identities are satisfied: \[ 0'=1,\quad 1'=0,\quad (x\vee y)'= x'\wedge y',\quad (x\wedge y)''= x''\wedge y'',\quad x'''= x'. \] The authors characterize those semi-De Morgan algebras which have only principal congruences (Theorem 3.14). In particular all such algebras are finite. The paper extends some of the results obtained by \textit{R. Beazer} [Port. Math. 50, 75-86 (1993; Zbl 0801.06023)].