CHAPTER 2 - COORDINATIZING BAER SEMIGROUPS

Abstract

This chapter describes the coordination of Baer semigroups. A class of lattices that arise in connection with certain rings is considered in the chapter. The chapter presents an example where the letters e, f, g, h (with or without subscripts) are used to denote idempotent elements of the ring A. If M ⊆ A, then R(M) = {x ∈ A; (V m ∈ M) mx = 0}. The set R(M) is called the right annihilator of M and is clearly a right ideal of A. Left annihilators are defined as one would expect and denoted by L(M) or L(x), whichever is appropriate. Any ring with an identity having no proper zero divisors is a Baer ring.