48 research outputs found
Powers of monomial ideals and the Ratliff-Rush operation
No full textPowers of (monomial) ideals is a subject that still calls attraction in various ways. In this paper we present a nice presentation of high powers of ideals in a certain class in K[x1, . . . , xn] and K[[x1, . . . , xn]]. As an interesting application it leads to an algorithm for computation of the Ratliff–Rush operation on ideals in that class. The Ratliff–Rush operation itself has several applications, for instance, if I is a regular m-primary ideal in a local ring (R, m), then the Ratliff–Rush associated ideal is the unique largest ideal containing I and having the same Hilbert polynomial as I
The 3-preprojective algebras of type Ã
No full textLet G ≤ SLn+1(C) act on R = C[X1, . . . , Xn+1] by change of variables. Then, the skew-group algebra R* G is bimodule (n + 1)-Calabi-Yau. In certain circumstances, this algebra admits a locally finite-dimensional grading of Gorenstein parameter 1, in which case it is the (n + 1)-preprojective algebra of its n-representation infinite degree 0 piece, as defined in [10]. If the group G is abelian, the (n +1)-preprojective algebra is said to be of type Ã. For a given group G, it is not obvious whether R* G admits such a grading making it into an (n + 1)-preprojective algebra. We study the case when n = 2 and G is abelian. We give an explicit classification of groups such that R* G is 3-preprojective by constructing such gradings. This is possible as long as G is not a subgroup of SL2(C) and not C2 x C2. For a fixed G, the algebra R* G admits different 3-preprojective gradings, so we associate a type to a grading and classify all types. Then we show that gradings of the same type are related by a certain kind of mutation. This gives a classification of 2-representation infinite algebras of type Ã. The involved quivers are those arising from hexagonal dimer models on the torus, and the gradings we consider correspond to perfect matchings on the dimer, or equivalently to periodic lozenge tilings of the plane. Consequently, we classify these tilings up to flips, which correspond to the mutation we consider
RINGS OF TETER TYPE
No full textLet R be a Cohen-Macaulay local K-algebra or a standard graded K-algebra over a field K with a canonical module omega(R). The trace of omega(R) is the ideal tr(omega(R)) of R which is the sum of those ideals phi(omega(R)) with phi is an element of Hom(R) (omega(R),R- ) . The smallest number s for which there exist phi(1),...,phi(s) is an element of Hom(R) (omega(R),R- ) with tr(omega(R)) = phi(1)(omega(R)) + ... + phi(s) (omega(R)) is called the Teter number of R. We say that R is of Teter type if s = 1. It is shown that R is not of Teter type if R is generically Gorenstein. In the present paper, we focus especially on zero-dimensional graded and monomial K-algebras and present various classes of such algebras which are of Teter type.</p
Implementatie Preconceptiezorg in Leiden; resultaten uit aanvullend kwalitatief onderzoek naar gepercipieerde effectieve wervingsstrategieën en de rol van het internet en nieuwe media
No full textEffect of Planting Density and Fertilizers on Productivity Potato Tubers
No full textThe results of experiments on accounting for planting density and the use of fertilizers are presented. The factors contributing to obtaining high quality and the potato crop with a sufficient amount of dry substances starch, high quality, the minimum content of nitrates and good condition of the tuber. An Amiri-600 potato variety was used in the experiment. The studies were conducted in 2014–2016. Of mineral fertilizers, ammonium nitrate, simple superphosphate, and potassium sulfate were used. As a result of the work, it was found that in the grey-brown (chestnut) irrigated soils of the Ganja–Gazakh zone of Azerbaijan, to obtain a high and high-quality crop of potato tubers, the optimal fertilizer dose is recommended — manure 20 t/ha+N90P120K90 kg/ha
The 3-preprojective algebras of type Ã
No full textLet G ≤ SLn+1(C) act on R = C[X1, ..., Xn+1] by change of variables. Then, the skew-group algebra R*G is bimodule (n+1)-Calabi-Yau. In certain circumstances, this algebra admits a locally finite-dimensional grading of Gorenstein parameter 1, in which case it is the (n+1)-preprojective algebra of its n-representation infinite degree 0 piece. If the group G is abelian, the (n+1)-preprojective algebra is said to be of type Ã. For a given group G, it is not obvious whether R*G admits such a grading making it into an (n+1)-preprojective algebra. We study the case when n=2 and G is abelian. We give an explicit classification of groups such that R*G is 3-preprojective by constructing such gradings. This is possible as long as G is not a subgroup of SL2(C) and not C2 x C2. For a fixed G, the algebra R*G admits different 3-preprojective gradings, so we associate a type to a grading and classify all types. Then we show that gradings of the same type are related by a certain kind of mutation. This gives a classification of 2-representation infinite algebras of type Ã. The involved quivers are those arising from hexagonal dimer models on the torus, and the gradings we consider correspond to perfect matchings on the dimer, or equivalently to periodic lozenge tilings of the plane. Consequently, we classify these tilings up to flips, which correspond to the mutation we consider.Oleksandra Gasanova, Universität Duisburg-Essen, is co-author of the included work</p
The 3-preprojective algebras of type Ã
No full textLet G ≤ SLn+1(C) act on R = C[X1, ..., Xn+1] by change of variables. Then, the skew-group algebra R*G is bimodule (n+1)-Calabi-Yau. In certain circumstances, this algebra admits a locally finite-dimensional grading of Gorenstein parameter 1, in which case it is the (n+1)-preprojective algebra of its n-representation infinite degree 0 piece. If the group G is abelian, the (n+1)-preprojective algebra is said to be of type Ã. For a given group G, it is not obvious whether R*G admits such a grading making it into an (n+1)-preprojective algebra. We study the case when n=2 and G is abelian. We give an explicit classification of groups such that R*G is 3-preprojective by constructing such gradings. This is possible as long as G is not a subgroup of SL2(C) and not C2 x C2. For a fixed G, the algebra R*G admits different 3-preprojective gradings, so we associate a type to a grading and classify all types. Then we show that gradings of the same type are related by a certain kind of mutation. This gives a classification of 2-representation infinite algebras of type Ã. The involved quivers are those arising from hexagonal dimer models on the torus, and the gradings we consider correspond to perfect matchings on the dimer, or equivalently to periodic lozenge tilings of the plane. Consequently, we classify these tilings up to flips, which correspond to the mutation we consider.Oleksandra Gasanova, Universität Duisburg-Essen, is co-author of the included work</p
Enveromental problems of Vestern Caspean agricural landskape. Ways of their decision
No full textStruggle against desertification of Northwest Caspian territories, ajonsidewith prevention of natural fodder lands degradation, should from agricultural system of pure streams and ground machining. Land improvement with use of Sorghum vulgare P., Medicago sateva L., Elytrigia elongata, Agrohyrum Pestiniforme R. is perspective for desrease of aoils salinity
On the Rees algebra and the conductor of an ideal
Get PDFFor an ideal in a Noetherian ring , we introduce and study its conductor as a tool to explore the Rees algebra of . The conductor of is an ideal obtained from the defining ideals of the Rees algebra and the symmetric algebra of by a colon operation. Using this concept we investigate when adding an element to an ideal preserves the property of being of linear type. In this regard, a generalization of a result by Valla in terms of the conductor ideal is presented. When the conductor of a graded ideal in a polynomial ring is the graded maximal ideal, a criteria is given for when the Rees algebra and the symmetric algebra have the same Krull dimension. Finally, noting the fact that the conductor of a monomial ideal is a monomial ideal, the conductor of some families of monomial ideals, namely bounded Veronese ideals and edge ideals of graphs, are determined.16 pages, 1 figur
The formation of juvenile pedagogy as an educational effort in the socialization of adolescents
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