A Problem of B. Plotkin for S-Acts: Automorphisms of Categories of Free S-Acts

Abstract

In this article, we prove that all automorphisms of categories of free S-acts are semi-inner, which solves a variation of Problem 12 in Plotkin (2002) for monoids. We also give a description of automorphisms of categories of finitely generated free algebras of varieties of unary algebras, and show that among varieties of unary algebras, only the variety of mono-unary algebras is perfect (Mashevitzky et al., 2002).

Key Words:

• Free S-acts over monoids
• Semi-inner automorphism
• Unary algebras

2000 Mathematics Subject Classification:

• Primary 08A60, 20M30, 20M99
• Secondary 08A35, 08C05, 20M50

Notes

Communicated by E. I. Zelmanov.