Simple Module
In mathematics, specifically in ring theory, the simple modules over a ring R are the (left or right) modules over R which have no non-zero proper submodules. Equivalently, a module M is simple if and only if every cyclic submodule generated by a non-zero element of M equals M. Simple modules form building blocks for the modules of finite length, and they are analogous to the simple groups in group theory.
In this article, all modules will be assumed to be right unital modules over a ring R.
Read more about Simple Module: Examples, Basic Properties of Simple Modules, Simple Modules and Composition Series, The Jacobson Density Theorem
Famous quotes containing the word simple:
“Geez, if I could get through to you, kiddo, that depression is not sobbing and crying and giving vent, it is plain and simple reduction of feeling. Reduction, see? Of all feeling. People who keep stiff upper lips find that it’s damn hard to smile.”
—Judith Guest (b. 1936)