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1	On the Characterization of Prime Sets of Polynomials by Congruence Conditions Suresh, Arvind 01 January 2015 (has links) This project is concerned with the set of primes modulo which some monic, irreducible polynomial over the integers has a root, called the Prime Set of the polynomial. We completely characterise these sets for degree 2 polynomials, and develop sufficient machinery from algebraic number theory to show that if the Galois group of a monic, irreducible polynomial over the integers is abelian, then its Prime Set can be written as the union of primes in some congruence classes modulo some integer. Number theory prime set polynomials algebraic integers congruence Number Theory
2	Algebraic Numbers and Topologically Equivalent Measures Huang, Kuoduo 12 1900 (has links) A set-theoretical point of view to study algebraic numbers has been introduced. We extend a result of Navarro-Bermudez concerning shift invariant measures in the Cantor space which are topologically equivalent to shift invariant measures which correspond to some algebraic integers. It is known that any transcendental numbers and rational numbers in the unit interval are not binomial. We proved that there are algebraic numbers of degree greater than two so that they are binomial numbers. Algebraic integers of degree 2 are proved not to be binomial numbers. A few compositive relations having to do with algebraic numbers on the unit interval have been studied; for instance, rationally related, integrally related, binomially related, B1-related relations. A formula between binomial numbers and binomial coefficients has been stated. A generalized algebraic equation related to topologically equivalent measures has also been stated. algebraic integers binomial numbers algebraic topology Algebraic fields. Algebraic topology.
3	Video Processing using multiplierless 2D-DCT with Algebraic Integers and MR-DCT Nimmalapalli, Sushmabhargavi January 2018 (has links) No description available. Electrical Engineering Image processing Loeffler factorization Algebraic integers 2D-DCT MR-DCT multiplierless
4	Digital Hardware Architectures for Exact and Approximate DCT Computation Using Number Theoretic Techniques Edirisuriya, Amila 21 May 2013 (has links) No description available. Electrical Engineering Computer Engineering DCT Algebraic integers Digital architecture FPGA ASIC
5	Sobre uma classificação dos anéis de inteiros, dos semigrupos finitos e dos RA-loops com a propriedade hiperbólica / On a classification of the integral rings, finite semigroups and RA-loops with the hyperbolic property Souza Filho, Antonio Calixto de 16 November 2006 (has links) Apresentamos duas construções para unidades de uma ordem em uma classe de álgebras de quatérnios que é anel de divisão: as unidades de Pell e as unidades de Gauss. Classificamos os anéis de inteiros de extensões quadráticas racionais, $R$, cujo grupo de unidades $\\U (R G)$ é hiperbólico para um certo grupo $G$ fixado. Também classificamos os semigrupos finitos $S$, tal que, para a álgebra unitária $\\Q S$ e para toda $\\Z$-ordem $\\Gamma$ de $\\Q S$, o grupo de unidades $\\U (\\Gamma)$ é hiperbólico. Nesse mesmo contexto, classificamos os {\\it RA}-loops $L$ cujo loop de unidades $\\U (\\Z L)$ não contém um subgrupo abeliano livre de posto dois. / For a given division algebra of a quaternion algebra, we construct and define two types of units of its $\\Z$-orders: Pell units and Gauss units. Also, for the quadratic imaginary extensions over the racionals and some fixed group $G$, we classify the algebraic integral rings for which the unit group ring is a hyperbolic group. We also classify the finite semigroups $S$, for which all integral orders $\\Gamma$ of $\\Q S$ have hyperbolic unit group $\\U(\\Gamma)$. We conclude with the classification of the $RA$-loops $L$ for which the unit loop of its integral loop ring does not contain a free abelian subgroup of rank two. álgebra de semigrupo álgebra dos quatérnios algebraic integers anel de grupo group group ring grupo grupo hiperbólico hyperbolic group inteiros algébricos loop loop ordens orders quaternion algebra semigroup semigroup algebra semigrupo structure theorem teorema de estrutura unidade unit
6	Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field Rezola, Nolberto 01 June 2015 (has links) The ring of integers is a very interesting ring, it has the amazing property that each of its elements may be expressed uniquely, up to order, as a product of prime elements. Unfortunately, not every ring possesses this property for its elements. The work of mathematicians like Kummer and Dedekind lead to the study of a special type of ring, which we now call a Dedekind domain, where even though unique prime factorization of elements may fail, the ideals of a Dedekind domain still enjoy the property of unique prime factorization into a product of prime ideals, up to order of the factors. This thesis seeks to establish the unique prime ideal factorization of ideals in a special type of Dedekind domain: the ring of algebraic integers of an imaginary quadratic number field. imaginary quadratic number field unique prime ideal factorization Dedekind domain Algebraic integers Rings Fields Ideals Integral over R-modules finitely generated set UFD PID. Algebra Number Theory Other Mathematics
7	Sobre uma classificação dos anéis de inteiros, dos semigrupos finitos e dos RA-loops com a propriedade hiperbólica / On a classification of the integral rings, finite semigroups and RA-loops with the hyperbolic property Antonio Calixto de Souza Filho 16 November 2006 (has links) Apresentamos duas construções para unidades de uma ordem em uma classe de álgebras de quatérnios que é anel de divisão: as unidades de Pell e as unidades de Gauss. Classificamos os anéis de inteiros de extensões quadráticas racionais, $R$, cujo grupo de unidades $\\U (R G)$ é hiperbólico para um certo grupo $G$ fixado. Também classificamos os semigrupos finitos $S$, tal que, para a álgebra unitária $\\Q S$ e para toda $\\Z$-ordem $\\Gamma$ de $\\Q S$, o grupo de unidades $\\U (\\Gamma)$ é hiperbólico. Nesse mesmo contexto, classificamos os {\\it RA}-loops $L$ cujo loop de unidades $\\U (\\Z L)$ não contém um subgrupo abeliano livre de posto dois. / For a given division algebra of a quaternion algebra, we construct and define two types of units of its $\\Z$-orders: Pell units and Gauss units. Also, for the quadratic imaginary extensions over the racionals and some fixed group $G$, we classify the algebraic integral rings for which the unit group ring is a hyperbolic group. We also classify the finite semigroups $S$, for which all integral orders $\\Gamma$ of $\\Q S$ have hyperbolic unit group $\\U(\\Gamma)$. We conclude with the classification of the $RA$-loops $L$ for which the unit loop of its integral loop ring does not contain a free abelian subgroup of rank two. álgebra de semigrupo álgebra dos quatérnios anel de grupo grupo grupo hiperbólico inteiros algébricos loop ordens semigrupo teorema de estrutura unidade algebraic integers group group ring hyperbolic group loop orders quaternion algebra semigroup semigroup algebra structure theorem unit
8	C-algebras from actions of congruence monoids Bruce, Chris* 20 April 2020 (has links) We initiate the study of a new class of semigroup C-algebras arising from number-theoretic considerations; namely, we generalize the construction of Cuntz, Deninger, and Laca by considering the left regular C-algebras of ax+b-semigroups from actions of congruence monoids on rings of algebraic integers in number fields. Our motivation for considering actions of congruence monoids comes from class field theory and work on Bost–Connes type systems. We give two presentations and a groupoid model for these algebras, and establish a faithfulness criterion for their representations. We then explicitly compute the primitive ideal space, give a semigroup crossed product description of the boundary quotient, and prove that the construction is functorial in the appropriate sense. These C-algebras carry canonical time evolutions, so that our construction also produces a new class of C-dynamical systems. We classify the KMS (equilibrium) states for this canonical time evolution, and show that there are several phase transitions whose complexity depends on properties of a generalized ideal class group. We compute the type of all high temperature KMS states, and consider several related C-dynamical systems. / Graduate C-algebras Semigroup C-algebras Operator algebras Primitive ideals KMS states C-dynamical system Number fields Rings of algebraic integers Congruence monoids von Neumann algebras Noncommutative geometry Faithful representations Groupoid C*-algebras Type III_1 factors

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