The first part of this paper investigates a class of homogeneously presented monoids. Constructions which enable division and multiplication to be computed are described. The word problem and the division problem are solved, and a unique normal form is given for monoids in this class. The second part deals with the motivating examples of this class-the positive singular Artin monoids. Finally, the singular Artin monoids are introduced. The: word and division problems are solved for all singular Artin monoids of finite type, including, for example, the singular braid monoids introduced by Baez and Birman. (C) 2000 Academic Press. [References: 14]
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