mathematics, the category of rings, denoted by Ring, is the category whose objects are rings (with identity) and whose morphisms are ring homomorphisms (that...

of the category of modules.) Category of rings Derived category Module spectrum Category of graded vector spaces Category of abelian groups Category of...

theory of algebraic geometry. Note: In the definition of a ringed space, most expositions tend to restrict the rings to be commutative rings, including...

mathematics, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism is...

examples include Set, the category of sets and set functions; Ring, the category of rings and ring homomorphisms; and Top, the category of topological spaces...

specifically in category theory, a preadditive category is another name for an Ab-category, i.e., a category that is enriched over the category of abelian groups...

Kampen theorem of algebraic topology (see below). In CRing, the category of commutative rings (a full subcategory of the category of rings), the pushout...

in the category of rings. Since direct products are defined up to an isomorphism, one says colloquially that a ring is the product of some rings if it...

ideas of algebraic number theory and algebraic geometry. The simplest commutative rings are those that admit division by non-zero elements; such rings are...

is a module category in the old sense over the commutative ring OX(X). One can also consider modules over a semiring. Modules over rings are abelian groups...