e/Nowhere commutative semigroup

Information
has gloss	eng: In mathematics, a nowhere commutative semigroup is a semigroup S such that, for all a and b in S, if ab = ba then a = b. A semigroup S is nowhere commutative if and only if any two elements of S are inverses of each other. : S is nowhere commutative. S is a rectangular band (in the sense in which the term is used by Howie ). For all a and b in S, aba = a. For all a, b and c in S, a2 = a and abc = ac.
lexicalization	eng: nowhere commutative semigroup
instance of	e/Algebraic structure