On exponential semigroups, I
Takayuki Tamura, John Shafer · Proceedings of the Japan Academy Series A Mathematical Sciences · 1972
exponential, G is exponential, and hence abelian.Let N--S/I be the Rees factor semigroup.Since archimedeaness is preserved by homomorphisms, N is an exponential, archimedean semigroup with zero 0. It is easy to see that N is nil.Remark.Recently M. S. Putcha has determined the biggest class of semigroups S each of which is a semilattice of archimedean semi- groups.The following condition characterizes S.If a, b e S, a divides b, then a divides some power of b.