On the relationship between the problems of equality and divisibility of words for semigroups with a single defining relation

摘要

Some results on the i-dutum-ship btttwwn the equality mid divisibility of words are obtained for one-relator semigroups. In particular, one of the main nssuStn in this i>ai>w is a, Unworn on tho oquivuleucc of the following three algorithmic problems: thu equality, the divisibility on the; left, and the divisibility on tho. right of words in .semigroups dufuux by a relation of the form a = hQa, where Q is a word in the letters u and b.