Infinite iteration of matrix semigroups II. Structure theorem for arbitrary semigroups up to aperiodic morphism

Abstract

(where 0 is defined by (a,,..., a,)8= a,. .. a,.) Here intuitively A + is “easily globally computed” because concatenation of two strings is a transparent multiplication and A + < A + i s surely special. However, here 0 need not be “line’‘-the unsolvability of the word problem for semigroups is one way to state this; we shall formulate it differently later (in fact, using the 25 0021-8693/86 $3.00