Maximal Normal Orthogroups in Rings Containing No Infinite Semilattices

ABSTRACT

Let R be a ring regarded as a multiplicative semigroup which contains no infinite subsemilattices. We investigate subsemigroups of R which are normal orthogroups, and present a construction from which all such maximal normal orthogroups can be obtained. In particular, we construct all maximal normal orthogroups of matrices over a field under matrix multiplication.

Communicated by D. Easdown.

Keywords:

• Completely regular semigroups
• Multiplicative semigroups of ring
• Orthogroups

Mathematics Subject Classification:

• 20M25