Rees factor

Let I be an ideal of a semigroupPlanetmathPlanetmath S. Define a congruencePlanetmathPlanetmathPlanetmathPlanetmath by xy iff x=y or x,yI.

Then the Rees factor of S by I is the quotient S/. As a matter of notation, the congruence is normally suppressed, and the quotient is simply written S/I.

Note that a Rees factor always has a zero element. Intuitively, the quotient identifies all element in I and the resulting element is a zero element.

Title Rees factor
Canonical name ReesFactor
Date of creation 2013-03-22 13:05:46
Last modified on 2013-03-22 13:05:46
Owner mclase (549)
Last modified by mclase (549)
Numerical id 4
Author mclase (549)
Entry type Definition
Classification msc 20M12
Classification msc 20M10
Related topic Ideal3