On Base Radical Operators for Classes of Finite Associative Rings

Abstract

In this paper, class operators are used to give a complete listing of distinct base radical and semisimple classes for universal classes of finite associative rings. General relations between operators reveal that the maximum order of the semigroup formed is 46. In this setting, the homomorphically closed semisimple classes are precisely the hereditary radical classes and hence radical–semisimple classes, and the largest homomorphically closed subclass of a semisimple class is a radical–semisimple class.

Idempotents and one-sided units: Lattice invariants and a semigroup of functors on the category of monoids

“…The author would like to acknowledge some valuable comments and questions from a number of colleagues, particularly Robert McDougal, Nik Ruškuc, Finn Smith, Timothy Stokes and Lauren Thornton. The idea to consider the semigroup F + traces back to conversations with Dr Thornton about her work on semigroups of operators on radical classes of rings and algebras [56,67].…”