• Honam Mathematical Journal
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• v.40 no.3
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• pp.539-548
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• 2018

The notions of Smarandache (positive implicative, commutative, implicative) d-algebras, Smarandache subalgebras of Smarandache d-algebras and Smarandache BCK-ideals(d-ideals) of a Smarandache d-algebras are introduced. Examples are given, and several related properties are investigated.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.375-381
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• 2019

In this paper, we introduce an operation denoted by [$Br_e$], a bracket operation, which maps an arbitrary groupoid ($X,{\ast}$) on a set X to another groupoid $(X,{\bullet})=[Br_e](X,{\ast})$ which on groups corresponds to sending a pair of elements (x, y) of X to its commutator $xyx^{-1}y^{-1}$. When applied to classes such as d-algebras, BCK-algebras, a variety of results is obtained indicating that this construction is more generally useful than merely for groups where it is of fundamental importance.