Thesis (Ph. D.)--University of Chicago, 1937. / Vita. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois."

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Neste trabalho, estudamos a multiplicidade de Hilbert-Samuel, e suas possíveis generalizações, tais como números de Segre e a sequência de multiplicidades de Achilles e Manaresi / In this work is studied the multiplicity of Hilbert-Samuel and its possible generalizations, such as Segre numbers and sequence of multiplicities of Achilles and Manaresi

This thesis exhibits a collection of proofs of theorems on ideals in a commutative ring with and without a unity. Theorems treated involve properties of ideals under certain operations (sum, product, quotient, intersection, and union); properties of homomorphic mappings of ideals; contraction and extension theorems concerning ideals and quotient rings of domains with respect to multiplicative systems; properties of maximal, minimal, prime, semi-prime, and primary ideals; properties of radicals of ideals with relations to quotient rings, semi-prime, and primary ideals.

The primary objective of this thesis is to present a unified account of the various generalizations of the concept of ring of quotients given by K, Asano (1949), R. E. Johnson (1951), Y. Utumi (1956), G. D. Findlay and J. Lambek (1958). A secondary objective is to investigate how far the commutative localization can be carried over to the noncommutative case. We begin with a formulation of the notion of D-system of right ideals of a ring R. The investigation of the D-systems was motivated by the fact that each maximal right quotient ring of R consists precisely of semi R-homomorphisms into R with domains in a specific D-system of right ideals of R or of R¹, the ring obtained from R by adjoining identity. A nonempty family X of right ideals of R is called a D-system provided the following three conditions holds: D1. Every right ideal of R containing some member of X is in X. D2. For any two right ideals A and B of R belonging to X, φ⁻¹B belongs to X for each R-homomorphism φ of A into R. D3. If A belongs to X and if for each a in A there exists Ba in X, then the ideal sum of aBa (a in A) is in X, Each D-system X of right ideals of R induces a modular closure operation on the lattice L(M) of all submodules of an R-module M and hence gives rise to a set Lx(M) of closed submodules of M. We are able to set up an isomorphism between the lattice of all modular closure operations on L(R) and the lattice of all D-systems of right ideals of R and characterize the D-systems X used in Asano's, Johnson's and Uturai's constructions of«quotient rings in terms of properties of Lx(R). In view of the intimate relation between the rings of quotients of a ring R and the extensions of R-modules, we generalize the concepts of infective R-module, rational and essential extensions of an R-module corresponding to a D-system T of right ideals of R¹. The existence and uniqueness of the maximal Y-essential extension, minimal Y-injective extension and maximal Y-rational extension of an R-module and their mutual relations are established. Finally, we come to the actual constructions of various extensions of rings and modules. The discussions center around the centralizer of a ring over a module, the maximal essential and rational extensions and the different types of rings of right quotients. We include here also a partial, though not satisfactory, solution of the noncommutative localization problem. / Science, Faculty of / Mathematics, Department of / Graduate

In [ASTW] it was given a Gröbner reduction based division formula for entire functions by polynomial ideals. Here we give degree bounds where the input function can be truncated in order to compute approximations of the coeffcients of the power series appearing in the division formula within a given precision. In addition, this method can be applied to the approximation of the value of the remainder function at some point.

In [ASTW] it was given a Gröbner reduction based division formula for entire functions by polynomial ideals. Here we give degree bounds where the input function can be truncated in order to compute approximations of the coeffcients of the power series appearing in the division formula within a given precision. In addition, this method can be applied to the approximation of the value of the remainder function at some point.

archives@tulane.edu / 1 / Abu Thomas

No description available.

No description available.