Abstract
This study introduces the concept of companion \emph{B}-algebra and establishes some of its properties. Also, this paper introduces the notions of $\odot$-subalgebra and $\odot$-ideal of a companion \emph{B}-algebra and investigates their relationship. Furthermore, this study establishes some homomorphic properties of $\odot$-subalgebra and $\odot$-ideal.
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