In this paper we introduce the notion of a super commutative d-algebra and we show that if (X; ∗) is a commutative binary system, then by adjoining an element 0 and adjusting the multiplication to x∗x = 0, we obtain a super commutative d-algebra, thereby demonstrating that the class of such algebras is very large. We also note that the class of super commutative d-algebras is Smarandache disjoint from the class of BCK-algebras, once more indicating that the class of d-algebras is quite a bit larger than the class of BCK-algeras and leaving the problem of finding further classes of d-algebras of special types which are Smarandache disjoint from the classes of BCK-algebras and super commutative d-algebras as an open question. Lastly the idea of a super Smarandache class of algebras is also defined and investigated.
[1]
K. Iseki.
An introduction to the theory of BCK-algebra
,
1978
.
[2]
K. Iseki,et al.
AN INTRODUCTION TO THE THEORY OF THE BCK-ALGEBRAS
,
1978
.
[3]
Y. B. Jun,et al.
On BH-algebras
,
1998
.
[4]
H. Kim,et al.
On $d$-algebras
,
1999
.
[5]
On B-algebras and quasigroups
,
2001
.
[6]
Joseph Neggers,et al.
On B-algebras
,
2002
.
[7]
W. B. Vasantha Kandasamy,et al.
Smarandache semirings and semifields
,
2010
.
[8]
P. J. Allen,et al.
SMARANDACHE DISJOINT IN BCK/D-ALGEBRAS
,
2004
.