An Introduction to Infinite Primes and Partial Orders for Rings
Buch in deiner Nähe kaufen
Beschreibung
This textbook provides a self-contained introduction to a developing area at the intersection of ring theory and order theory. Beginning with foundational concepts and results, it explores the connections between infinite primes, maximal partial orders, symmetric partial orders, and directed orders in fields, integral domains, and more general commutative rings. Topics include embedding theorems, Archimedean and strong Archimedean orders, partial orders on complex numbers and quaternions, rings with negative squares, Dedekind σ-complete partially ordered rings, O*-fields, and L*-rings. Each chapter concludes with exercises that reinforce the theory, illustrate key constructions, and highlight open questions for further investigation. Written for graduate students and researchers with a background in abstract algebra, this text combines foundational material and modern developments, offering an accessible entry point into this area of research.
This textbook provides a self-contained introduction to a developing area at the intersection of ring theory and order theory. Beginning with foundational concepts and results, it explores the connections between infinite primes, maximal partial orders, symmetric partial orders, and directed orders in fields, integral domains, and more general commutative rings. Topics include embedding theorems, Archimedean and strong Archimedean orders, partial orders on complex numbers and quaternions, rings with negative squares, Dedekind σ-complete partially ordered rings, O*-fields, and L*-rings. Each chapter concludes with exercises that reinforce the theory, illustrate key constructions, and highlight open questions for further investigation. Written for graduate students and researchers with a background in abstract algebra, this text combines foundational material and modern developments, offering an accessible entry point into this area of research.
Combines classical results with modern developments, providing a bridge from foundational theory to current research Includes exercises and open problems that provide entry points for further study and research Presents a unified framework for infinite primes and ordered structures
Autor*in
Jingjing Ma
Themen in »An Introduction to Infinite Primes and Partial Orders for Rings«
Maximal Partial Orders Symmetric Partial Orders Ordered Rings and Fields Order Extensions O*-Fields L*-Rings Infinite Primes