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On the subdirectly irreducible semi-De Morgan algebras. (English) Zbl 0868.06006
The authors deal with questions relevant to the equational class of semi-De Morgan algebras. Particularly interesting is a characterization of the subdirectly irreducible algebras, which the authors attain by the congruence \(\varphi\) of the homomorphism \(x\to x''\). Indeed it is proven that a semi-De Morgan algebra \(L\) is a subdirectly irreducible algebra if and only if it is a subdirectly irreducible De Morgan algebra or \(\varphi\) is the minimum element of the nontrivial congruences on \(L\). Moreover, the coherent semi-De Morgan algebras and the coherent demi \(p\)-lattices are characterized.
Reviewer: A.Di Nola (Napoli)

06D15 Pseudocomplemented lattices
06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
06D99 Distributive lattices
08A30 Subalgebras, congruence relations
08B26 Subdirect products and subdirect irreducibility