Integral closure of a quartic extension

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）=z^4＋az^2＋bz＋c over R.We 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 z^4＋a（x）z^2＋b（x）z＋c（x）=0.The integral closure is expressed as a syzygy module and the syzygy equations are given explicitly.We compute also the ramifications of the integral closure over R.