Abstract
Diagrams have been used in group theory by numerous authors, and have led to significant results (see [4] and the references cited there). The idea of applying diagrams to semigroups seems to be more recent [3, 7, 8]. In the present paper we discuss semi group diagrams and use them to obtain results concerning the word problem for one-relator semigroups. The word problem for one-relatorgroupshas been solved by Magnus [6], but the analogous question for semigroups remains open. We are not able to solve the problem in full generality, but have obtained some partial results.
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