ABSTRACT STRUCTURES
in Category Theory
May 2006; published online September 2007.
Chapter. Subjects: algebra. 7868 words.
This chapter focuses on abstract characterizations. It is shown that one of the basic ways of giving abstract characterization is via a Universal Mapping Property (UMP). Epis and monos, initial and...
ADJOINTS
in Category Theory
May 2006; published online September 2007.
Chapter. Subjects: algebra. 14099 words.
This chapter focuses on notion of adjoint functor, which applies everything that has been learned so far to unify and subsume all the different universal mapping properties encountered, from free...
Algorithmic aspects
in The Diophantine Frobenius Problem
December 2005; published online September 2007.
Chapter. Subjects: algebra. 11104 words.
This chapter is devoted to the computational aspects of the Frobenius number. After discussing a number of methods to solve FP when n = 3 (some of these procedures make use of diverse concepts, such...
Applications of the Frobenius number
in The Diophantine Frobenius Problem
December 2005; published online September 2007.
Chapter. Subjects: algebra. 10982 words.
This chapter presents a number of applications of FP to a variety of problems. The complexity analysis of the Shellsort method was not well understood until J. Incerpi and R. Sedgewick nicely...
AUTOMORPHIC FORMS ON INNER FORMS OF GL(2)
in Hilbert Modular Forms and Iwasawa Theory
June 2006; published online September 2007.
Chapter. Subjects: algebra. 62652 words.
This chapter is an exposition of the ideas and classical (and modern) results of the theory for Hilbert modular forms and quaternionic automorphic forms. It starts with a brief exposition of the...
CATEGORIES
in Category Theory
May 2006; published online September 2007.
Chapter. Subjects: algebra. 8344 words.
This chapter begins with a discussion of category theory, which can be defined as the mathematical study of (abstract) algebras of functions. The functions of sets, definitions of a category,...
CATEGORIES OF DIAGRAMS
in Category Theory
May 2006; published online September 2007.
Chapter. Subjects: algebra. 6911 words.
This chapter presents the proof for the Yoneda Lemma, which is probably the single most used result in category theory. It is interesting how often it comes up, especially in view of the fact that it...
Category Theory
May 2006; published online September 2007.
Book. Subjects: algebra. 272 pages.
This book is a text and reference book on Category Theory, a branch of abstract algebra. The book contains clear definitions of the essential concepts, which are illuminated with numerous accessible...
Completely integrally closed modules and rings
in Cyclic Modules and the Structure of Rings
September 2012; published online January 2013.
Chapter. Subjects: algebra. 6295 words.
This chapter presents a brief study of completely integrally closed modules and rings.
Cyclic Modules and the Structure of Rings
September 2012; published online January 2013.
Book. Subjects: algebra. 232 pages.
This book provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a...