伪BCK-代数和伪BCI-代数的一些性质
Some properties of pseudo-BCK- and pseudo-BCI-algebras
摘要：
伪BCI-代数推广了BCI-代数和伪BCK-代数，它们是BCK-代数的非交换推广。在本文中，继[J.G. Raftery和C. J. van Alten，具有最小零的交换有序幺半群中的剩余，Rep. Math. Log。34（2000）23-57]中，证明了伪BCI-代数是半整剩余po-monoid的剩余次约简，并刻画了伪BCI-代数是伪BCK-代数与群的直积（称为伪BCI-代数）.我们还表明，伪BCI-代数的拟簇是相对同余模;事实上，我们证明，这适用于所有相对点正则拟簇是相对理想的确定，在这个意义上，相对同余的内核可以描述的理想条款。
英文摘要：
Pseudo-BCI-algebras generalize both BCI-algebras and pseudo-BCK-algebras, which are a non-commutative generalization of BCK-algebras. In this paper, following [J.G. Raftery and C.J. van Alten, Residuation in commutative ordered monoids with minimal zero, Rep. Math. Log. 34 (2000) 23-57], 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.
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