Get Math Help

GET TUTORING NEAR ME!

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Irreducible Module

    Alternate name
    Definition

    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.

    Related term

    irreducible ring

    Find the right fit or it’s free.

    We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.