Integral closure of a quartic extension

作     者：TAN ShengLi XIE DaJun 

作者机构：Department of Mathematics and Shanghai Key Laboratory of PMMP East China Normal University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2015年第58卷第3期

页      面：553-564页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11231003) the Science Foundation of Shanghai(Grant No.13DZ2260600) East China Normal University Reward for Excellent Doctors in Academics(Grant No.XRZZ2012014) 

主　　题：algebraic invariants quartic extension integral closure discriminant syzygy 

摘      要：Let R be a Noetherian unique factorization domain such that 2 and 3 are units,and let A=R[α]be a quartic extension over R by adding a rootαof an irreducible quartic polynomial p(z)=z4+az2+bz+c over *** will compute explicitly the integral closure of A in its fraction field,which is based on a proper factorization of the coefficients and the algebraic invariants of p(z).In fact,we get the factorization by resolving the singularities of a plane curve defined by z4+a(x)z2+b(x)z+c(x)=*** integral closure is expressed as a syzygy module and the syzygy equations are given *** compute also the ramifications of the integral closure over R.