A Proof of Wedderburn's Theorem

• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 证明 定理 有限域 有限维
• 年，卷（期）: 2015,（4）
• 页码范围: 603-606
• 页数: 4页
• 分类号: O174
• 语种: 中文

摘要

In this note we first introduce the finite weak Herstein condition, which is a property that holds for every finite field. For a field F satisfying the finite weak Herstein condition, we then characterize whether all the finite-dimensional division F-algebras are commutative. This gives an alternate proof of Wedderburn's Theorem.