module homomorphism

模同态

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

Translation evidence: Literature usage

Meaning in context

An additive map f:M→Nf:M\to N between left RR-modules satisfying f(rm)=rf(m)f(rm)=rf(m).

在同一环的左模之间保持加法与标量作用的映射。

Example

Multiplication by 22 is a Z\mathbb Z-module map Z→Z\mathbb Z\to\mathbb Z.

Usage and distinctions

The scalar ring must be specified; additive maps are only automatically Z\mathbb Z-linear.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source基本概念, definition of 模同态 for φ:M_1→M_2 between left R-modules, additive and scalar-preservation clauses · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件基本概念, definition of 模同态 for φ:M_1→M_2 between left R-modules, additive and scalar-preservation clauses · Checked 2026-10-15
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