Concept

# Principal ideal

Summary
In mathematics, specifically ring theory, a principal ideal is an ideal I in a ring R that is generated by a single element a of R through multiplication by every element of R. The term also has another, similar meaning in order theory, where it refers to an (order) ideal in a poset P generated by a single element x \in P, which is to say the set of all elements less than or equal to x in P. The remainder of this article addresses the ring-theoretic concept. Definitions
• a left principal ideal of R is a subset of R given by Ra = {ra : r \in R} for some element a,
• a right principal ideal of R is a subset of R given by aR = {ar : r \in R} for some element a,
• a two-sided principal ideal of R is a subset of R given by R
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications (3)

Related people

Related units