Simple Extensions with the Minimum Degree Relations of Integral Domains, Vol. 253 Book

BIRATIONAL SIMPLE EXTENSIONS The Ring R[a] n R[a-1]
Anti-Integral Extension and Flat Simple Extensions The Ring R(Ia) and the Anti-Integrality of a Strictly Closedness and Integral Extensions Upper-Prime, Upper-Primary, or Upper-Quasi-Primary Ideals Some Subsets of Spec(R) in the Birational Case

SIMPLE EXTENSIONS OF HIGH DEGREE Sharma Polynomials Anti-Integral Elements and Super-Primitive Elements Integrality and Flatness of Anti-Integral Extensions Anti-Integrality of a and a-1
Vanishing Points and Blowing-Up Points

SUBRINGS OF ANTI-INTEGRAL EXTENSIONS Extensions R[a] n R[a-1] of Noetherian Domains R The Integral Closedness of the Ring R[a] n R[a-1] (I)
The Integral Closedness of the Ring R[a] n R[a-1] (II)
Extensions of Type R[ß] n R[ß-1] with ß ? K(a)

DENOMINATOR IDEALS AND EXCELLENT ELEMENTS Denominator Ideals and Flatness (I)
Excellent Elements of Anti-Integral Extensions Flatness and LCM-Stableness Some Subsets of Spec(R) in the High Degree Case

UNRAMIFIED EXTENSIONS Unramifiedness and Etaleness of Super-Primitive Extensions Differential Modules of Anti-Integral Extensions Kernels of Derivations on Simple Extensions

THE UNIT GROUPS OF EXTENSIONS The Unit-Groups of Anti-Integral Extensions Invertible Elements of Super-Primitive Ring Extensions

EXCLUSIVE EXTENSIONS OF NOETHERIAN DOMAINS Subring R[a] n K of Anti-Integral Extensions Exclusive Extensions and Integral Extensions An Exclusive Extension Generated by a Super-Primitive Element Finite Generation of an Intersection R[a] n K over R Pure Extensions

ULTRA-PRIMITIVE EXTENSIONS AND THEIR GENERATORS Super-Primitive Elements and Ultra-Primitive Elements Comparisons of Subrings of Type R[aa] n R[(aa)-1]
Subrings of Type R[Ha] n R[(Ha)-1]
A Linear Generator of an Ultra-Primitive Extension R[a]
Two Generators of Simple Extensions

FLATNESS AND CONTRACTIONS OF IDEALS Flatness of a Birational Extension Flatness of a Non-Birational Extension Anti-Integral Elements and Coefficients of its Minimal Polynomial Denominator Ideals and Flatness (II)
Contractions of Principal Ideals and Denominator Ideals

ANTI-INTEGRAL IDEALS AND SUPER-PRIMITIVE POLYNOMIALS Anti-Integral Ideals and Super-Primitive Ideals Super-Primitive Polynomials and Sharma Polynomials Anti-Integral, Super-Primitive, or Flat Polynomials

SEMI ANTI-INTEGRAL AND PSEUDO-SIMPLE EXTENSIONS Anti-Integral Extensions of Polynomial Rings Subrings of R[a] Associated with Ideals of R Semi Anti-Integral Elements Pseudo-Simple Extensions

REFERENCES INDEX