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 ex

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.