Minimal ideal

In the branch of abstract algebra known as ring theory, a minimal right ideal of a ring R is a nonzero right ideal which contains no other nonzero right ideal. Likewise a minimal left ideal is a nonzero left ideal of R containing no other nonzero left ideals of R, and a minimal ideal of R is a nonzero ideal containing no other nonzero two-sided ideal of R. (Isaacs 2009, p.190)