We investigate factorization of elements in overrings of a half-factorial domain in relation with the behaviour of the boundary map of . It turns out that a condition, called , on the extension plays a central role in this study. We finally apply our results to the special case of polynomial rings.
In rings of formal power series in several variables whose growth of coefficients is controlled by a suitable sequence (such as rings of Gevrey series), we find precise estimates for quotients F/Φ, where F and Φ are series in such that F is divisible by Φ in the usual ring of all power series. We give first a simple proof of the fact that F/Φ belongs also to , provided is stable under derivation. By a further development of the method, we obtain the main result of the paper, stating that...
One gives a formula for the calculation of the local intersection multiplicity index of analytic varieties, analogous to the Bézout formula in the case of algebraic varieties in the projective space, in the case of normal crossings. One obtains also a recurrent process for the calculation of the local intersection multiplicity index of plane analytic curves.
Let be a non-maximal order in a finite algebraic number field with integral closure . Although is not a unique factorization domain, we obtain a positive integer and a family (called a Cale basis) of primary irreducible elements of such that has a unique factorization into elements of for each coprime with the conductor of . Moreover, this property holds for each nonzero when the natural map is bijective. This last condition is actually equivalent to several properties linked...
For a finite Coxeter group and a Coxeter element of ; the -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of . Its maximal cones are naturally indexed by the -sortable elements of . The main result of this paper is that the known bijection cl between -sortable elements and -clusters induces a combinatorial isomorphism of fans. In particular, the -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for . The rays...
We give Lambek-Carlitz type characterization for completely multiplicative reduced incidence functions in Möbius categories of full binomial type. The -analog of the Lambek-Carlitz type characterization of exponential series is also established.
Let be a field and a finite-dimensional -algebra of global dimension . We construct a triangulated category associated to which, if is hereditary, is triangle equivalent to the cluster category of . When is Hom-finite, we prove that it is 2-CY and endowed with a canonical cluster-tilting object. This new class of categories contains some of the stable categories of modules over a preprojective algebra studied by Geiss-Leclerc-Schröer and by Buan-Iyama-Reiten-Scott. Our results also...