ring theory

The term ‘**ring theory**’ usually refers to the study of classical (not necessarily commutative) rings, unital or not, and often also of modules over them.

Some of the related entries in nlab include noetherian ring, maximal spectrum, prime spectrum, commutative algebra, prime ideal, ideal, filter, Ore set, Gabriel filter, primitive ideal?, Schur's lemma.

Generalizations of rings include rigs, $\Omega$-groups, generalized rings in the sense of Durov, associative algebras over a commutative ring; moreover additive categories can be considered as a horizontal categorification of unital rings; and once upon a time they were called *rings with many objects*.