polynomial ring

多项式环

Algebra & Algebraic Geometry · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

For a commutative ring $R$, the ring $R[x]$ of finite formal sums $\sum a_ix^i$ with coefficientwise addition and convolution multiplication.

以交换环为系数、由有限形式和构成并按多项式规则运算的环。

Example

$x^2+1\in\mathbb F_2[x]$.

Usage and distinctions

Over a finite field distinct formal polynomials may induce the same polynomial function.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Wen-Wei Li — Methods in Algebra I, author source从幺半群环到多项式环 (sec:polynomial-ring), definition headed 多项式环 with one-variable specialization; def:monoidal-ring supplies finite coefficients and convolution multiplication · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件从幺半群环到多项式环 (sec:polynomial-ring), definition headed 多项式环 with one-variable specialization; def:monoidal-ring supplies finite coefficients and convolution multiplication · Checked 2026-10-15

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