modular ideal

Let R be a ring. A left idealMathworldPlanetmathPlanetmath I of R is said to be modular if there is an eR such that re-rI for all rR. In other words, e acts as a right identityPlanetmathPlanetmath element modulo I:


A right modular ideal is defined similarly, with e be a left identity modulo I.

Remark. If an ideal I is modular both as a left ideal as well as a right ideal in R, then R/I is a unital ring. Furthermore, every (left, right, two-sided) ideal in a unital ring is modular, implying that the notion of modular ideals is only interesting in rings without 1.


  • 1 P. M. Cohn, Further Algebra and Applications, Springer (2003).
Title modular ideal
Canonical name ModularIdeal
Date of creation 2013-03-22 17:31:47
Last modified on 2013-03-22 17:31:47
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 7
Author CWoo (3771)
Entry type Definition
Classification msc 16D25