Abstract
In this paper, we consider a collection of d*-ideals of a d-algebra D. We use the connotation of congruence relation regard to d*-ideals to construct a uniformity which induces a topology on D. We debate the properties of this topology.
Highlights
Yoon and Kim [4] and Meng and Jun [5] introduced two classes of abstract algebras: namely, BCK-algebras and BCI-algebras
It is known that the class of BCK algebras is a proper subclass of the class of BCI-algebras
In [2], [3] Bourbaki and Sims introduced a wide class of abstract algebras: BCH-algebras
Summary
Yoon and Kim [4] and Meng and Jun [5] introduced two classes of abstract algebras: namely, BCK-algebras and BCI-algebras. In [2], [3] Bourbaki and Sims introduced a wide class of abstract algebras: BCH-algebras. They have shown that the class of BCIalgebras is a proper subclass of the class of BCH-algebras. Neggers et al [6] introduced the notion of d-algebras which is another generalization of BCK-algebras, and investigated relations between d-algebras and BCK-algebras. They studied the various topologies in a manner analogous to the study of lattices. It turns out that we may use the class of d-ideals of a d-algebra as the underlying structure whence a certain uniformity and thence a topology is derived which provides a natural connection between the notion of a d-algebra and the notion of a topology in that we are able to conclude that in this setting a d-algebra becomes a topological d-algebra
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