On Radical Congruence Systems II

Abstract

This paper is a continuation of a paper of the same title by the first author and P. Weil. We first characterize the universal class of a radical congruence system. We then introduce the meet and the (limit) iteration of congruence systems. This enables us to generate new radical congruence systems from given congruence systems. Some interesting examples are presented. We finally determine the smallest radical congruence systems whose universal classes are N, LZ o N, RZ o N, and RB o N respectively.

Decomposition of the lattice of pseudovarieties of finite semigroups induced by bands

“…For a comprehensive bibliography, the reader is referred to Petrich and Reilly [19]. A series of recent papers, Reilly and Zhang [25], Auinger, Hall, Reilly and Zhang [3], Auinger [2], Hall and Weil [11], Hall and Zhang [12], Pastijn and Trotter [18] and Trotter and Weil [29], has explored the extension of these ideas, first to the lattice of existence varieties of regular semigroups and then to the lattice of pseudovarieties of finite semigroups. Some of these complete congruences on L(CR) are induced by mappings of the form V −→ V ∩ X for some special variety X , such as the variety of groups, completely simple semigroups or bands (see Jones [15], Trotter [28] or Reilly [23]).…”