tensor product of modules

模的张量积

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

Translation evidence: Literature usage

Meaning in context

For a right $R$-module $M$ and left $R$-module $N$, the abelian group representing biadditive maps satisfying $b(mr,n)=b(m,rn)$.

对右模与左模，由满足标量平衡条件的双加性映射所表出的阿贝尔群。

Example

$(\mathbb Z/4)\otimes_{\mathbb Z}(\mathbb Z/6)\cong\mathbb Z/2$.

Usage and distinctions

Elements are finite sums of pure tensors; not every element is a single pure tensor.

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Definition sources

1. Wen-Wei Li — Methods in Algebra I, author source模的张量积 (sec:module-tensor-prod), definitions def:balanced-product and def:tensor-product, balanced biadditive maps and universal property · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件模的张量积 (sec:module-tensor-prod), definitions def:balanced-product and def:tensor-product, balanced biadditive maps and universal property · Checked 2026-10-15

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