simple module

A nonzero module M over a ring R whose only submodules are the module itself and the zero module. It is also called a simple module, and in fact this is the name more frequently used nowadays (Rowen, 1988). Behrens' definition includes the additional condition that R M be not the zero module. Sometimes, the term irreducible is used as an abbreviation for meet-irreducible, which means that the intersection of two nonzero submodules is always nonzero.

irreducible ring