The semigroups of binary systems and some perspectives
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Given binary operations “*” and “◦” on a set X, define a product binary operation “∗” as follows: x∗y := (x * y) ◦ (y * x). This in turn yields a binary operation on Bin(X), the set of groupoids defined on X turning it into a semigroup (Bin(X), ∗)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 ∗ 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.
Abstract
Given binary operations “*” and “◦” on a set X, define a product binary operation “∗” as follows: x∗y := (x * y) ◦ (y * x). This in turn yields a binary operation on Bin(X), the set of groupoids defined on X turning it into a semigroup (Bin(X), ∗)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 ∗ 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.
참고문헌 (11)
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