Category of rings | StudentB Wikipedia Search

Algebraic structure → Ring theory Ring theory
Basic concepts Rings • Subrings • Ideal • Quotient ring • Fractional ideal • Total ring of fractions • Product of rings • Free product of associative algebras • Tensor product of algebras Ring homomorphisms • Kernel • Inner automorphism • Frobenius endomorphism Algebraic structures • Module • Associative algebra • Graded ring • Involutive ring • Category of rings • Initial ring $\mathbb {Z}$ • Terminal ring $0=\mathbb {Z} /1\mathbb {Z}$ Related structures • Field • Finite field • Non-associative ring • Lie ring • Jordan ring • Semiring • Semifield
Commutative algebra Commutative rings • Integral domain • Integrally closed domain • GCD domain • Unique factorization domain • Principal ideal domain • Euclidean domain • Field • Finite field • Polynomial ring • Formal power series ring Algebraic number theory • Algebraic number field • Integers modulo $n$ • Ring of integers • p-adic integers $\mathbb {Z} _{p}$ • p-adic numbers $\mathbb {Q} _{p}$ • Prüfer p-ring $\mathbb {Z} (p^{\infty })$
Noncommutative algebra Noncommutative rings • Division ring • Semiprimitive ring • Simple ring • Commutator Noncommutative algebraic geometry Free algebra Clifford algebra • Geometric algebra Operator algebra
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In mathematics, the category of rings, denoted by Ring, is the category whose objects are rings (with identity) and whose morphisms are ring homomorphisms (that preserve the identity). Like many categories in mathematics, the category of rings is large, meaning that the class of all rings is proper.