Composition ring information

Algebraic structure → Ring theory Ring theory
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Commutative algebra Commutative rings • Integral domain • Integrally closed domain • GCD domain • Unique factorization domain • Principal ideal domain • Euclidean domain • Field • Finite field • Composition ring • Polynomial ring • Formal power series ring Algebraic number theory • Algebraic number field • Ring of integers • Algebraic independence • Transcendental number theory • Transcendence degree p-adic number theory and decimals • Direct limit/Inverse limit • Zero ring $\mathbb {Z} /1\mathbb {Z}$ • Integers modulo pⁿ $\mathbb {Z} /p^{n}\mathbb {Z}$ • Prüfer p-ring $\mathbb {Z} (p^{\infty })$ • Base-p circle ring $\mathbb {T}$ • Base-p integers $\mathbb {Z}$ • p-adic rationals $\mathbb {Z} [1/p]$ • Base-p real numbers $\mathbb {R}$ • p-adic integers $\mathbb {Z} _{p}$ • p-adic numbers $\mathbb {Q} _{p}$ • p-adic solenoid $\mathbb {T} _{p}$ Algebraic geometry • Affine variety
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In mathematics, a composition ring, introduced in (Adler 1962), is a commutative ring (R, 0, +, −, ·), possibly without an identity 1 (see non-unital ring), together with an operation

\circ :R\times R\rightarrow R

such that, for any three elements $f,g,h\in R$ one has

$(f+g)\circ h=(f\circ h)+(g\circ h)$
$(f\cdot g)\circ h=(f\circ h)\cdot (g\circ h)$
$(f\circ g)\circ h=f\circ (g\circ h).$

It is not generally the case that $f\circ g=g\circ f$ , nor is it generally the case that $f\circ (g+h)$ (or $f\circ (g\cdot h)$ ) has any algebraic relationship to $f\circ g$ and $f\circ h$ .

Composition ring information

and 22 Related for: Composition ring information

Composition ring

Function composition

Ring homomorphism

Chiastic structure

Polynomial ring

Commutative ring

Semiring

Composition operator

Ring theory

Quotient ring

Zero ring

Noncommutative ring

Composition series

Formal power series

Integer

Associative algebra

Ring of integers

Integral domain

Commutative algebra

Field of fractions

Endomorphism ring

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