What does it mean for a relation algebra to be simple?

Question

I am reading "Boolean Algebras with Operators part II" by Bjarni Jonsson and Alfred Tarski. On theorem 4.10 (p.132-133), they refer to a relation algebra $\mathfrak{A}$ being "simple" and proves that it is equivalent to $\mathfrak{A}$ having no ideal elements different from 0 and 1. What definition of "simple" is being used in this context? The article is in JSTOR, by the way.

Answer 1

According to the definitions given in the extended abstract available here, a simple relation algebra is one that satisfies the condition $1;r;1=1$ for every non-zero $r$, where ‘;’ is the composition operator. Apparently an ideal element is an element $r$ that satisfies $1;r;1=r$.