Kurosh–Amitsur Radicals via a Weakened Galois Connection

Abstract

In the present paper we consider a correspondence weaker than Galois connection and prove that this produces Kurosh–Amitsur radicals in a very general setting including all universal classes of Ω-groups. As a framework we introduce a simple combinatorial structure which uses mappings between complete lattices.

Key Words:

• Kurosh-Amitsur radical
• Galois connection
• complete lattice
• Cominatorial exactness structure

Acknowledgments

Research of the first author was partially supported by a visiting professorship of the Paul Erdös Summer Research Center (Hungary). Hospitality of the University of Aveiro (Portugal) is also gratefully acknowledged. Research of the second author was supported partly by the Hungarian National Foundation for Scientific Research grants no. T29525 and T34530.