Semisimple Classes of Semirings

• 来源期刊: 代数集刊（英文版）
• 关键词: semiring radical theory semisimple class
• 年，卷（期）: 2002,（2）
• 页码范围: 177-196
• 页数: 20页
• 语种: 英文

摘要

A famous result of Sands states that a class S of associative rings is semisimple if and only if S is regular, coinductive, and extensionally closed. Here,we investigate semisimple classes in a Kurosh-Amitsur radical theory for semirings. We show that such a class S is regular, K-coinductive, and K-extensionally closed. But a characterization of semisimple classes of semirings needs a fourth condition, namely that S is inverse semi-isomorphically closed. We also obtain other characterizations and results for semisimple classes and for subdirect products of semirings.