A minimal left ideal of a ring 
is a nonzero left ideal that contains
no nonzero proper left ideal. Minimal right ideals and minimal two-sided ideals are
defined analogously. If 
has an identity, every minimal left ideal has the form 
for a primitive idempotent 
when 
is semisimple Artinian.
Minimal Ideal
See also
Ideal, Maximal Ideal, Simple RingExplore with Wolfram|Alpha
References
Lam, T. Y. A First Course in Noncommutative Rings, 2nd ed. New York: Springer-Verlag, 2001.Cite this as:
Weisstein, Eric W. "Minimal Ideal." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MinimalIdeal.html