In the branches of abstract algebra known as ring theory and module theory, each right (resp.

In module theory, one replaces the field of scalars by a ring.

The concepts of linear independence, span, basis, and dimension (which is called rank in module theory) still make sense.

Nevertheless, many theorems from linear algebra become false in module theory.

It allows the adaptation of many results from matrix theory and module theory.

His earlier work was mostly in module theory, especially torsion theories, non-commutative localization, and injective modules.

In mathematics, specifically module theory, annihilators are a concept that generalizes torsion and orthogonal complement.

Artinian serial rings are sometimes called Nakayama algebras, and they have a well-developed module theory.

Both constructions are universal and translate representation theory into module theory.

One of the approaches to representations of finite groups is through module theory.