an:06955099
Zbl 1397.06028
Emanovsk??, Petr; K??hr, Jan
Some properties of pseudo-BCK- and pseudo-BCI-algebras
EN
Fuzzy Sets Syst. 339, 1-16 (2018).
00416601
2018
j
06F35
pseudo-BCK-algebra; pseudo-BCI-algebra; filter; prefilter; ideal term; relative congruence modularity
Summary: Pseudo-BCI-algebras generalize both BCI-algebras and pseudo-BCK-algebras, which are a non-commutative generalization of BCK-algebras. In this paper, following \textit{J. G. Raftery} and \textit{C. J. van Alten} [Rep. Math. Logic 34, 23--57 (2000; Zbl 0996.03040)], we show that pseudo-BCI-algebras are the residuation subreducts of semi-integral residuated po-monoids and characterize those pseudo-BCI-algebras which are direct products of pseudo-BCK-algebras and groups (regarded as pseudo-BCI-algebras). We also show that the quasivariety of pseudo-BCI-algebras is relatively congruence modular; in fact, we prove that this holds true for all relatively point regular quasivarieties which are relatively ideal determined, in the sense that the kernels of relative congruences can be described by means of ideal terms.
Zbl 0996.03040