Abstract
Small cancellation theory has been an important tool in group theory. Remmers [R] in his thesis has applied some of the techniques to show that a finitely presented semigroupS has a solvable word problem if the presentation satisfiesC(3). In this paper, which was part of the doctoral dissertation [C] of the first named author, we show that the word problem forS is solvable ifS is finitely presented and satisfiesC(2) andT(4). This completes the analogy with the small cancellation hypotheses in group theory, see for example [LS], Chapter V. The authors would like to express their gratitude to the referee for pointing out a mistake in the original manuscript and suggesting the correct definition ofT(4).
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