Groupoid Factorizations in the Semigroup of Binary Systems

zbMATH Open1506.20094arXiv2010.09229MaRDI QIDQ5104413

Hiba F. Fayoumi

Publication date: 9 September 2022

Abstract: Let $$ be a groupoid (binary algebra) and $Bin(Xdot)$ denote the collection of all groupoids defined on $X$. We introduce two methods of factorization for this binary system under the binary groupoid product extquotedblleft $diamond$ extquotedblright in the semigroup $left(Binleft(Xight),diamondight)$. We conclude that a strong non-idempotent groupoid can be represented as a product of its extit{% similar-} and extit{signature-} derived factors. Moreover, we show that a groupoid with the orientation property is a product of its extit{orient-} and extit{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.

Full work available at URL: https://arxiv.org/abs/2010.09229

zbMATH Keywords

idempotent groupoid\(\mathrm{Bin}(X)\)\(\Psi\)-type-factor\(\tau\)-type-factorcomposite groupoidgroupoid decompositiongroupoid factorizationj-normalorient-factorprime groupoidsignature-factorsimilar-factorskew-factoru-normal

Mathematics Subject Classification ID

BCK-algebras, BCI-algebras (06F35) Sets with a single binary operation (groupoids) (20N02)

Related Items (1)

Independence concepts for groupoids

This page was built for publication: Groupoid Factorizations in the Semigroup of Binary Systems

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5104413)