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Showing 1 to 20 of 56 for “"Divisor"”.
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Zero Divisor Graphs and Poset Decomposition
… ring R where the vertices are the non-zero zero divisors of R with two vertices adjacent if x · y = 0. The zero-divisor graph has also been studied for various algebraic stuctures such as semigroups and partially ordered sets. In this paper, we will discuss some known results on zero-divisor …
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Analytic versions of the zero divisor conjecture
… and frustrating problems in algebra is the zero divisor conjecture. In this work we study some analytical versions of this conjecture. We will give sufficient conditions to determine when elements of CG are uniform non zero divisors, we also give sufficient conditions to determine when elements …
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Partitions into prime powers and related divisor functions
In this thesis, we will study a class of divisor functions: the prime symmetric functions. These are polynomials over Q in the so-called elementary prime symmetric functions, whose values lie in Z. The latter are defined on the nonnegative integers and take the values of the elementary symmetric …
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A study of homological invariants modulo an exact zero divisor
… ring of Q by an ideal generated by an exact zero divisor. We use differential graded structures to describe a construction that produces a minimal free resolution of an R-module from the free resolution of the same module, considered as a Q-module, and the free resolution of R as a Q-module. We …
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Characterizations Of Zero Divisor Graphs Determined By Equivalence Classes Of Zero Divisors
We study zero divisor graphs of commutative rings determined by equivalence classes of zero divisors, specifically for a Noetherian ring R. We study the classification of these graphs. Specifically, we add more criteria to the list of characterizations that disqualify a graph as the zero divisor …
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The Behavior on the Restriction of Divisor Classes to Sequences of Hypersurfaces
… A/ fnA satisfies R1. We establish the map of divisor classes jn*: Cl(A) → Cl((A/fnA)'), where (A/fnA)' represents the integral closure, and investigate the injectivity of jn*. The first result shows that no nontrivial divisor class can lie in every kernel. Secondly, when A is an isolated …
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Comparison of and Improvements to Degree Zero Divisor Class Group Arithmetic in Algebraic Function Fields
This thesis develops improved algorithms for Jacobian arithmetic in global function fields and compares the improvements to previous works. We present two independent improvements to Jacobian arithmetic based on the unique representation described in [13]. The first improvement requires the …
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Hypersurface Sections: A Study of Divisor Class Groups and of the Complexity of Tensor Products
The second part concerns the notion of complexity, a measure of the growth of the Betti numbers of a module. We show that over a complete intersection R the complexity of the tensor product $M\otimes\sb{R}N$ of two finitely generated modules is the sum of the complexities of each if …
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On the Average Order of the Divisor Function, Lattice Point Functions, and Other Arithmetical Functions
We consider a large class of arithmetical functions generated by Dirichlet series satisfying a very general functional equation with gamma factors. We obtain one and two-sided (OMEGA)-theorems for the error terms associated with certain weighted averages of these arithmetical functions. For …
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Divisor de águas no Rio do Peixe: ambientalização dos conflitos sociais e racismo ambiental vivenciados pelos comunitários do Quati - Ba
The central theme of this dissertation is the intersection between social conflicts and racial relations in the Quati Community, in the municipality of Pedro Alexandre, Bahia. The aim is to understand the conflicts and environmental racism experienced by the members of the Quati community before, …
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Infrastructure, Arithmetic, and Class Number Computations in Purely Cubic Function Fields of Characteristic at Least 5
Finally, we describe methods to compute the divisor class number, h, of K, and in the case that O has unit rank 1 or 2, the regulator and ideal class number of O as well. A method of Scheidler and Stein [SS07, SS08] determines sharper upper and lower bounds on h, for a given cubic function field, …
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Zero Divisors, Group Von Neumann Algebras and Injective Modules
… which is intimately related to the zero divisor conjecture. We also discuss the square integrable representations of the generalized Wyle-Heisenberg group in 𝑛² dimensions and its relations with Gabor's question from Gabor Analysis in the light of the time-frequency equation. We study the …
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The topology of terminal quartic 3-folds
… theorem states that any Cartier divisor on Y is the restriction of a Cartier divisor on P^4 . However, no such result holds for the group of Weil divisors. More generally, let Y be a terminal Gorenstein Fano 3-fold with Picard rank 1. Denote by s(Y )=h_4 (Y )-h^2 (Y ) = h_4 (Y )-1 …
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Excess Porteous, Coherent Porteous, and the Hyperelliptic Locus in M3
… 3, the locus of hyperelliptic curves forms a divisor, that is a closed subscheme of codimension 1. J. Harris and I. Morrison compute an expression for the class of this divisor, in the Chow ring of the moduli space, using a map of vector bundles and by applying the Thom-Porteous formula to …
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Localization of Divisors of Integers and of Some Arithmetic Functions
… of positive integers n ≤ x having exactly two divisors in ( y, z], in the range of y10 ≤ z ≤ x1/3, and that of the function H3(x, y, z), the number of positive integers n ≤ x having exactly three divisors in ( y, z], in the range of y10 ≤ z ≤ x1/4. Next, we introduce a new …
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The Severi problem for rational curves on del Pezzo surfaces
… C on X. Let VC be the set of all irreducible divisors on X linearly equivalent to C whose normalization is a rational curve. The Severi problem for rational curves on X with divisor class [C] consists of studying the irreducibility of the spaces VC as C varies among all curves on X. In this …
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Deformation invariance of rational pairs
… Here X is a normal variety and D is a reduced divisor on X. Integral to the definition of a rational pair is the notion of a thrifty resolution, also defined by Kollár and Kovács, and in order to work with rational pairs it is often necessary to know whether a given resolution is thrifty. In …
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Floer cohomology in the mirror of the projective plane and a binodal cubic curve
… with a binodal cubic curve as anticanonical divisor. These objects correspond under mirror symmetry to the powers of the twisting sheaf 0(1), and hence their Floer cohomology groups form an algebra isomorphic to the homogeneous coordinate ring. An interesting feature is the presence of a …
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Numerical properties of pseudo-effective divisors
… that X is a smooth variety and L is an effective divisor. One of the main goals of bi rational geometry is to understand the asymptotic behavior of the linear series... as m increases. The two most important features of the asymptotic behavior - the litaka dimension and the litaka fibration - are …
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Asymptotic behavior of complete Ricci-flat metrics on open manifolds
… can be compactified by adding a smooth, ample divisor. This result provides an answer to a question addressed to by Tian and Yau in [TY1], therefore refining the main result in that paper.
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