Simple Extensions with the Minimum Degree Relations of Integral Domains
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A01=Ken-ichi Yoshida
A01=Susumu Oda
advanced simple extension properties
algebraic
Algebraic Field Extension
anti-integral
Anti-integral Element
Author_Ken-ichi Yoshida
Author_Susumu Oda
birational simple extensions
birational theory
Category=PBF
commutative algebra
denominator ideals
element
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exact Sequence
Excellent Element
field
Finitely Generated
flat module theory
ideal contraction
Infinite Field
integral domains
Invertible Ideal
krull
Krull Domain
Maximal Ideal
minimal
Minimal Polynomial
Minimal Prime Divisors
Monic Polynomial
noetherian
Noetherian domain
Noetherian Integral Domain
Noetherian Normal Domain
Nonzero Element
polynomial
Polynomial Ring
Primary Decomposition
Prime Divisor
Prime Ideal
Principal Ideal
quotient
Quotient Field
R
Ramification Locus
ring
Sharma polynomial analysis
Susumu Oda
unit group structure
Unramified Extension
Product details
- ISBN 9781584888512
- Weight: 432g
- Dimensions: 156 x 234mm
- Publication Date: 05 Mar 2007
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Paperback
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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.
Kochi University, Japan Okayama University of Science, Japan
