On The Theory Of Brk-algebras

The notion of BRK-algebras were introduced by Ravi Kumar Ban-rndaru in 2012 as a generalization of BCK/BCI/BCH/Q-algebras. Hernobtained some properties of BRK-algebras by introducing the classi-rncal notions such as subalgebras and ideals. In this thesis we furtherrninvestigate the properties of BRK-algebras by considering homo-rnmorphisms, right maps, left maps and multipliers. We constructrnQuotient BRK-algebra using a special type of ideal called transla-rntion ideal. Moreover we introduce two new sub classes of BRK-rnalgebras, namely anti-symmetric BRK-algebras and weak positivernimplicative BRK-algebras that have special properties. Finally wernhave proved that nite direct product of BRK-algebras is again arnBRK-algebra and obtained certain properties.

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