Simple Extensions with the Minimum Degree Relations of Integral Domains
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.
