direct sum of modules

模的直和

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

Translation evidence: Literature usage

Meaning in context

The module of tuples from a family (Mi)(M_i) having only finitely many nonzero coordinates, with coordinatewise operations.

模族中仅有有限多个非零坐标的元组所构成的模，运算逐坐标进行。

Example

⨁n≥1Z\bigoplus_{n\ge1}\mathbb Z consists of finite-support integer sequences.

Usage and distinctions

For an infinite index set the direct product allows infinite support and differs from the direct sum.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source模的基本操作 (sec:mod-operations), proof of prop:module-cat-completeness, item 2, construction named 余积（直和）as finite-support tuples · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件模的基本操作 (sec:mod-operations), proof of prop:module-cat-completeness, item 2, construction named 余积（直和）as finite-support tuples · Checked 2026-10-15
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