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1	Length function on modules Vamos, Peter January 1968 (has links) No description available. 510 Commutative algebra, R-modules
2	R-Modules for the Alexander Cohomology Theory Anderson, Stuart Neal 05 1900 (has links) The Alexander Wallace Spanier cohomology theory associates with an arbitrary topological space an abelian group. In this paper, an arbitrary topological space is associated with an R-module. The construction of the R-module is similar to the Alexander Wallace Spanier construction of the abelian group. r-modules Alexander cohomology theory
3	Properties of R-Modules Granger, Ginger Thibodeaux 08 1900 (has links) This thesis investigates some of the properties of R-modules. The material is presented in three chapters. Definitions and theorems which are assumed are stated in Chapter I. Proofs of these theorems may be found in Zariski and Samuel, Commutative Algebra, Vol. I, 1958. It is assumed that the reader is familiar with the basic properties of commutative rings and ideals in rings. Properties of R-modules are developed in Chapter II. The most important results presented in this chapter include existence theorems for R-modules and properties of submodules in R-modules. The third and final chapter presents an example which illustrates how a ring R, may be regarded as an R-module and speaks of the direct sum of ideals of a ring as a direct sum of submodules. Commutative Algebra R-modules commutative rings Commutative rings. Ideals (Algebra)
4	Stabilizers of direct composition series Droste, Manfred, Göbel, Rüdiger 13 December 2018 (has links) Let R be a domain, V a left R-module, and L a composition series of direct summands of V. Our main results show that if U is a stabilizer group of L containing the McLain-group associated with L , then U determines the chain (L,⊆) uniquely up to isomorphism or anti-isomorphism.
5	SiGe HBT BiCMOS RF front-ends for radar systems Poh, Chung Hang 01 November 2011 (has links) The objective of this research is to explore the possibilities of developing transmit/receive (T/R) modules using silicon-germanium (SiGe) heterojunction bipolar transistor (HBT) BiCMOS technology to integrate with organic liquid crystal polymer (LCP) packages for the next-generation phased-array radar system. The T/R module requirements are low power, compact, lightweight, low cost, high performance, and high reliability. All these requirements have provided a very strong motivation for developing fully monolithic T/R modules. SiGe HBT BiCMOS technology is an excellent candidate to integrate all the RF circuit blocks on the T/R module into a single die and thus, reducing the overall cost and size of the phase-array radar system. In addition, this research also investigates the effects and the modeling issues of LCP package on the SiGe circuits at X-band. RF Front-ends T/R modules SiGe HBT BiCMOS LCP Radar RF Packaging Radar Materials Polymer liquid crystals Liquid crystals Bipolar transistors Transistors
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

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