Kim, Hee Sik; Neggers, Joseph The semigroups of binary systems and some perspectives. (English) Zbl 1172.20047 Bull. Korean Math. Soc. 45, No. 4, 651-661 (2008). Summary: Given binary operations “\(*\)” and “\(\circ\)” on a set \(X\), define a product binary operation “\(\square\)” as follows: \(x\square y:= (x*y)\circ(y*x)\). This in turn yields a binary operation on \(\text{Bin}(X)\), the set of groupoids defined on \(X\) turning it into a semigroup \((\text{Bin}(X),\square)\) with identity (\(x*y=x\)) the left zero semigroup and an analog of negative one in the right zero semigroup (\(x*y=y\)). The composition \(\square\) is a generalization of the composition of functions, modelled here as leftoids (\(x*y= f(x)\)), permitting one to study the dynamics of binary systems as well as a variety of other perspectives also of interest. Cited in 6 Documents MSC: 20N02 Sets with a single binary operation (groupoids) 08A02 Relational systems, laws of composition 20M99 Semigroups Keywords:semigroups of binary systems; leftoids; groupoids; orbits PDF BibTeX XML Cite \textit{H. S. Kim} and \textit{J. Neggers}, Bull. Korean Math. Soc. 45, No. 4, 651--661 (2008; Zbl 1172.20047) Full Text: DOI OpenURL