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Showing 1 to 20 of 55 for “"Monomial"”.
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Powers of Monomial Ideals
We study monomial ideals in polynomial rings in two variables x, y over a field K. We determine various monomial ideals I such that Ik = (Mn)k where M is the maximal ideal generated by x, y and k is the least such integer. This is related to the well-known notion of Ratliff-Rush closures of an …
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The Golod Property on Monomial Rings
… by Berglund and Jollenbeck which stated that a monomial ring is Golod if and only if the product on its Koszul Homology is trivial. At the end, we find a non-Golod monomial ring with trivial product on its Koszul homology, so we will need the backwards direction to be stronger in order for this …
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Monomial Dynamical Systems over Finite Fields
… in the theory of finite dynamical systems. For monomial dynamical systems, that is, a system that can be described by monomials, information about the limit cycles can be obtained from the monomials themselves. In particular, this work contains sufficient and necessary conditions for a monomial …
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Finite Generation of Ext-Algebras for Monomial Algebras
… finite generation of the cohomology rings of monomial algebras, and thereafter G. Davis determined a finite criteria for such generation in the case of cycle algebras. Herein, we describe the construction of a finite directed graph upon which criteria can be established to determine finite …
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Monomial Ideals, N-Lists, and Smallest Graded Betti Numbers
The second set of results in this thesis concerns the existence of smallest graded betti numbers. Given an Artinian Hilbert function H , consider all ideals I ⊂ R such that H(R/I) = H . Then the graded betti numbers which correspond to these ideals form a finite set which we partially order …
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Algebraic Reliability. Monomial ideals applied to multi-state system reliability
… un acercamiento algebraico basado en ideales monomiales. Consideramos un sistema como un conjunto de componentes junto con una función de estructura. Tanto las componentes como el sistema se dicen binarios si u ́nicamente pueden alcanzar dos niveles o estados de funcionamiento diferentes: 0 es …
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Normal Subgroups of Odd Order Monomial P(a)q(b)-Groups
A finite group G is called monomial if every irreducible character of G is induced from a linear character of some subgroup of G. One of the main questions regarding monomial groups is whether or not a normal subgroup N of a monomial group G is itself monomial. In the case that G is a group of even …
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Two interactions between combinatorics and representation theory : monomial immanants and Hochschild cohomology
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.
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Finite Generation of Ext-Algebras of Finite Dimensional Algebras and Associated Monomial Algebras
… which generate $I^!$. In the case $A$ is monomial, we prove that the family $\{f_i^m\}$ is exactly the set of $m$-chains used by Green and Zacharia. </p> <p> In the second part, we use a construction by Anick, Green, and Solberg to form a family $\{x_i^j\}$ which yields a projective …
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Combinatorial Koszul Homology: computations and Applications
… of the Koszul homology and Betti numbers of monomial ideals, the main goals od this thesis are the following: Analyze the Koszul homology of monomial ideals and apply it to describe the structure of monomial ideals. Describe algorithms to perform efficient computations of the homological …
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The Combinatorics of Involutive Bases: Theory, algorithms and applications
In this thesis, we conduct an in-depth study of monomial ideals and other related structures in commutative algebra. Our primary tool for exploring the connections between these algebraic objects and combinatorics is the use of involutive bases, along with other types of Gröbner bases that exhibit …
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On the Strong Direct Summand Conjecture
… In Chapter 4, we study the related Strong Monomial Conjecture. Extending work of Dutta, we give several reformulations of the Strong Monomial Conjecture and prove the Strong Monomial Conjecture for systems of parameters of a certain form. In Chapter 5, we present a generalization of the …
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On Decomposition of the Product of Demazure atoms and Demazure Characters
… property of the product of a dominating monomial and an atom, which was an open problem. Furthermore, it provides a combinatorial proof to the key-positivity property of the product of a dominating monomial and a key using skyline fillings, an algebraic proof to the key-positivity …
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Resolutions and cohomology of finite dimensional algebras
… Adding the extra hypothesis that A is a monomial algebra, we construct a minimal projective resolution of A over A e. The syzygies for this resolution exhibit an alternating behavior which is explained by the construction of a special sequence of paths from the quiver of A. Finally, a …
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Koszul Complexes, Local Cohomology, Universal Resolutions, and Cohomological Support Varieties
… its construction when resolving a quotient of a monomial ideal over a polynomial ring. We provide a construction for calculating support varieties of monomial ideals which is slightly more computationally manageable than any known construction. We use this to manually verify a computation of the …
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Domains of convergence in infinite dimensional holomorphy
… F(R), i.e. the set of all points of R where the monomial expansion \sum_{\alpha\in \N_0^{(\N)}} \frac{\partial^{\alpha} f (0)}{\alpha !} z^{\alpha} of every function f \in F(R) is (unconditionally) convergent. The results are obtained by an interplay of complex analysis and local Banach space …
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Progenitors Related to Simple Groups
… among their homomorphic images. We give the full monomial automorphism groups of Aut(3^{*2}), Aut(3^{*3}), and Aut(5^{*2}). Included is a proof showing that the full monomial automorphism group of Aut(m^{*n}) is isomorphic to U(m) wr S_n. In addition we have constructed the Cayley Diagrams of …
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Growth of algebras, words, and graphs
Finitely generated monomial algebras are studied. the bound in Bergman's description of algebras with GK-dimension 1 is improved and similar techniques are used to establish the equivalence of the periodicities of overlap graphs and Hilbert series coefficients.
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Grobner Bases and Ideals of Points
… a review of ideals, the definitions and types of monomial ordering, the multivariate polynomial division algorithm and its examples. After ascertaining the monomial ordering on multivariate polynomials, we establish a leading term of a polynomial.In Chapter 2, after defining Grobner bases, we …
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An analysis of posynomial MOSFET models using genetic algorithms and visualization
… modeled by the genetic algorithm and by monomial fitting. It concludes that posynomial MOSFET models suffer from inherent inaccuracies. Additionally, although genetic algorithms improve on the maximum model error, the improvement, in general, does not vastly surpass results obtained …
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