Simple Extensions with the Minimum Degree Relations of Integral Domains / Edition 1

by Susumu Oda, Ken-ichi Yoshida

Overview

Although there are many types of ring extensions, simple extensions have yet to be thoroughly explored in one book. Covering an understudied aspect of commutative algebra, Simple Extensions with the Minimum Degree Relations of Integral Domains presents a comprehensive treatment of various simple extensions and their properties. In particular, it examines several properties of simple ring extensions of Noetherian integral domains.

As experts who have been studying this field for over a decade, the authors present many arguments that they have developed themselves, mainly exploring anti-integral, super-primitive, and ultra-primitive extensions. Within this framework, they study certain properties, such as flatness, integrality, and unramifiedness. Some of the topics discussed include Sharma polynomials, vanishing points, Noetherian domains, denominator ideals, unit groups, and polynomial rings.

Presenting a complete treatment of each topic, Simple Extensions with the Minimum Degree Relations of Integral Domains serves as an ideal resource for graduate students and researchers involved in the area of commutative algebra.

Product Details

ISBN-13:	9781138401891
Publisher:	Taylor & Francis
Publication date:	01/03/2018
Series:	Lecture Notes in Pure and Applied Mathematics
Pages:	296
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Susumu Oda, Ken-ichi Yoshida

Table of Contents

Birational Simple Extensions. Simple Extensions of High Degree. Subrings of Anti-Integral Extensions. Denominator Ideals and Excellent Elements. Unramified Extensions. The Unit Groups of Extensions. Exclusive Extensions of Noetherian Domains. Ultra-Primitive Extensions and Their Generators. Flatness and Contractions of Ideals. Anti-Integral Ideals and Super Primitive Polynomials. Semi Anti-Integral and Pseudo-Simple Extensions. References. Index.

Editorial Reviews

"All topics … are developed in a clear way and illustrated by many examples."

– EMS Newsletter, September 2008

From the Publisher