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:
“The threadbare trees, so poor and thin,
They are no wealthier than I;
But with as brave a core within
They rear their boughs to the October sky.
Poor knights they are which bravely wait
The charge of Winter’s cavalry,
Keeping a simple Roman state,
Discumbered of their Persian luxury.”
—Henry David Thoreau (1817–1862)