Strong and Ordinary d-Algebras
Jeong Soon Han, Hee Sik Kim and J. Neggers
In this paper we define several special varieties of d-algebras, such as strong d-algebras, (weakly) selective d-algebras and others. In addition we deal with a generalization of d-algebras called pre-d-algebras. Much of our discussion involves the associative groupoid product (X; ) = (X; *) (X; ◦) where x y = (x * y) ◦ (y * x). One assertion is that the squared algebra (X; , 0) of a pre-d-algebra (X; *, 0) is a strong d-algebra if and only if (X; *, 0) is a strong d-algebra.
Keywords: (strong, pre-) d-algebra, BCK-algebra, product groupoid, squared algebra, (weakly) selective.
2000 Mathematics Subject Classification. 06F35.