Maximal Orders in Semigroups1
نویسندگان
چکیده
Inspired by the ring theory concepts of orders and classical rings of quotients, Fountain and Petrich introduced the notion of a completely 0-simple semigroup of quotients in [19]. This was generalised to a much wider class of semigroups by Gould in [20]. The notion extends the well known concept of group of quotients [8]. To give the definition we first have to explain what is meant by a square-cancellable element in a semigroup. Let a be an element of a semigroup S. We say that a is square-cancellable in S if for all x, y ∈ S, xa = ya implies that xa = ya
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