Clone Networks, Clone Extensions and Biregularizations of Varieties of Algebras

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: clone network variety biregular lattice
• 年，卷（期）: 2001,（3）
• 页码范围: 327-344
• 页数: 18页
• 分类号: O1
• 语种: 英文

摘要

We consider algebras of type τ- without nullary operations. An identity ψ≈ψ of type τ is clone compatible if ψ and ψ are the same variable or the sets of fundamental operation symbols in ψ and ψ are non-empty and identical. For a variety V, we denote by Vc the variety defined by all clone compatible identities from Id(V). In this paper, we give a construction of algebras called a clone network. Under some assumptions, we describe algebras from Vc by means of this construction. We find some properties of Vc and applications.