An I-semigroup [resp. I-monoid] is a semigroup S [resp. a monoid M] with a unary operation xx-1 defined on S [resp. on M] such that for each x,yS [resp. for each x,yM]


Notice that


so x-1 is an inverseMathworldPlanetmathPlanetmathPlanetmath of x.

The class of I-semigroups [resp. I-monoids] strictly contains the class of inverse semigroups [resp. inverse monoids]. In fact, the class of inverse semigroups [resp. inverse monoids] is precisely the class of I-semigroups with involution [resp. I-monoids with involution], i.e. the class of I-semigroups [resp. I-monoids] in which the unary operation -1 is also an involution.


  • 1 J.M. Howie, Fundamentals of Semigroup Theory, Oxford University Press, Oxford, 1991.
Title I-semigroup
Canonical name Isemigroup
Date of creation 2013-03-22 16:11:27
Last modified on 2013-03-22 16:11:27
Owner Mazzu (14365)
Last modified by Mazzu (14365)
Numerical id 5
Author Mazzu (14365)
Entry type Definition
Classification msc 20M10
Related topic SemigroupWithInvolution
Defines I-semigroup
Defines I-monoid