Classes of examples of pseudo-MV algebras, pseudo-BL algebras and divisible bounded non-commutative residuated lattices

摘要

We illustrate by classes of examples the close connections existing between pseudo-MV algebras, on the one hand, and pseudo-BL algebras and divisible bounded non-commutative residuated lattices, on the other hand. We use equivalent definitions of these algebras, as particular cases of pseudo-BCK algebras. We analyse the strongness, the pseudo-involutive center and the filters for each example. Keywords Pseudo-MV algebra - Pseudo-Wajsberg algebra - Pseudo-BCK algebra - Pseudo-BL algebra - Pseudo-Hájek(pP) algebra - Divisible bounded non-commutative residuated lattice - Divisible bounded pseudo-BCK(pP) lattice