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- W2055185582 abstract "This article studies commutative orders, that is, commutative semigroups having a semigroup of quotients. In a commutative order $$S$$ , the square-cancellable elements $$mathcal {S}(S)$$ constitute a well-behaved separable subsemigroup. Indeed, $$mathcal {S}(S)$$ is also an order and has a maximum semigroup of quotients $$R$$ , which is Clifford. We present a new characterisation of commutative orders in terms of semilattice decompositions of $$mathcal {S}(S)$$ and families of ideals of $$S$$ . We investigate the role of tensor products in constructing quotients, and show that all semigroups of quotients of $$S$$ are homomorphic images of the tensor product $$Rotimes _{mathcal {S}(S)} S$$ . By introducing the notions of generalised order and semigroup of generalised quotients, we show that if $$S$$ has a semigroup of generalised quotients, then it has a greatest one. For this we determine those semilattice congruences on $$mathcal {S}(S)$$ that are restrictions of congruences on $$S$$ ." @default.
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- W2055185582 date "2014-05-29" @default.
- W2055185582 modified "2023-10-14" @default.
- W2055185582 title "Commutative orders revisited" @default.
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- W2055185582 doi "https://doi.org/10.1007/s00233-014-9568-1" @default.
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