Groupoids with Only Linear Term Functions

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: groupoid term function term-linear affine spaces
• 年，卷（期）: 2001,（4）
• 页码范围: 427-440
• 页数: 14页
• 分类号: O1
• 语种: 英文

摘要

When one deals with terms over algebras, it is quite natural to look for the simplest terms which represent all the terms, and it will be very convenient for many reasons if every term can be represented by a linear term, as in the cases of modules, semilattices, Boolean groups, affine spaces, and so on. On the other hand, the linearity of terms imposes much restraint on the structure and properties of the algebra. We call an algebra term-linear if every term is equal to some linear term or constant function and every linear term is essential in the sense that it depends on each variable it involves. In this paper, we study some properties and identities of term-linear groupoids, and characterize term-linear semigroups and term-linear commutative idempotent groupoids.