Factor-Functions on Partially Ordered Sets and Reduced Incidence Algebras

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: factor-function partially ordered set reduced incidence algebra
• 年，卷（期）: 2001,（1）
• 页码范围: 109-120
• 页数: 12页
• 分类号: O1
• 语种: 英文

摘要

In this paper, we generalize the notion of "factor-function", originally introduced by Wiegandt [8], and obtain a family of not necessarily commutative algebras on partially ordered sets. Our algebras are then shown to be naturally isomorphic to certain reduced incidence algebras. We also show that a class of these algebras consists of homomorphic images of power series rings in non-commuting variables.