Groupoid Factorizations in the Semigroup of Binary Systems Article (Faculty180)

cited authors

  • Fayoumi, Hiba F

description

  • <p><span><strong>Abstract</strong></span><span>. </span><span>Let (X, •) be a groupoid (binary algebra) and Bin(X), denote the collection of all groupoids defined on X. We introduce two methods of factorization for this binary system under the binary groupoid product “<>” in the semigroup (Bin(X) , <>). We conclude that a strong non-idempotent groupoid can be represented as a product of its similar- and signature- derived factors. Moreover, we show that a groupoid with the orientation property is a product of its orient- and skew- factors. These unique factorizations can be useful for various applications in other areas of study. Application to algebras such as B/BCH/BCI/BCK/BH/BI/d-algebra are widely given throughout this paper.</span><span> </span></p>

authors

publication date

  • 2020

volume

  • e-2020