The KIWI project developed a platform called OntoExtractor enabling semi-automatic extraction of ontologies. This platform is composed of different modules. A first module extract typical instances from a data flow. A second module propose some topological relations among the detected classes. A third module assist the knowledge engineer in transforming classes and relations tentatively propose...

Let R be a right GF -closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorenstein ring R, the G...

Because of the associativity of fusion products ⊠, the above hypothesis is equivalent to the condition that for each irreducible module W , there is an irreducible module W̃ such that HomV (W̃ ⊠ W,V ) 6= 0. In the previous paper [6], we have introduced a concept of ”Semi-Rigidity” and then proved that if W is semi-rigid, then W is flat for the fusion products ⊠, that is, 0 → W ⊠ A → W ⊠ B → W ⊠ C...

In this paper we present a new approach to Grothendieck duality over commutative rings. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic geometry. The method of rigidity was modified to work over general commutative base rings in our paper [YZ5]. In the present paper we obtain many of the important l...

Let f : X → Y be a Cohen-Macaulay map of finite type between Noetherian schemes, and g : Y ′ → Y a base change map, with Y ′ Noetherian. Let f ′ : X → Y ′ be the base change of f under g and g : X → X the base change of g under f . We show that there is a canonical isomorphism θ g : g ∗ ωf ≃ ωf ′ , where ωf and ωf ′ are the relative dualizing sheaves. The map θ g f is easily described when f is...

The tropical semi-ring is the triplet (R,⊕, ) with x⊕ y := min(x,y) and x y := x+ y . Its algebraic properties are somewhat modest, if one compares it with rings and fields, which are more common in most areas of mathematics. Still the distributive laws hold, and as an additional catch the addition is idempotent, that is, x⊕ x = x holds for all x ∈ R. As defined our tropical semi-ring is lackin...

Abstract Let X be a semistable curve and L line bundle whose multidegree is uniform, i.e., in the range between those of structure sheaf dualizing . We establish an upper bound for $$h^0(X,L)$$ h 0 ( X , L</mml:m...