Aklilu, Girum2019-05-042023-11-042019-05-042023-11-042018-12-01http://etd.aau.edu.et/handle/123456789/18185The 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.enBRK-AlgebrasBCI-AlgebraSubalgebrasThesis