On the Theory of BRK-Algebras
No Thumbnail Available
Date
2018-12-01
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Addis Ababa University
Abstract
The notion of BRK-algebras were introduced by Ravi Kumar Ban-
daru in 2012 as a generalization of BCK/BCI/BCH/Q-algebras. He
obtained some properties of BRK-algebras by introducing the classi-
cal notions such as subalgebras and ideals. In this thesis we further
investigate the properties of BRK-algebras by considering homo-
morphisms, right maps, left maps and multipliers. We construct
Quotient BRK-algebra using a special type of ideal called transla-
tion ideal. Moreover we introduce two new sub classes of BRK-
algebras, namely anti-symmetric BRK-algebras and weak positive
implicative BRK-algebras that have special properties. Finally we
have proved that nite direct product of BRK-algebras is again a
BRK-algebra and obtained certain properties.
Description
Keywords
BRK-Algebras, BCI-Algebra, Subalgebras