Computation of inverses in residue class rings of parametric polynomial ideals
Computation of inverses in residue class rings of parametric polynomial ideals
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DOI：
10.1145/1576702.1576745
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发表时间：
2009-07
期刊：
影响因子：
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通讯作者：
Yosuke Sato;A. Suzuki
中科院分区：
文献类型：
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作者：
Yosuke Sato;A. Suzuki
For a given polynomial f and an ideal I of a polynomial ring K[X] over a field K, we give a necessary and sufficient condition for I to have a smallest ideal extension J such that f is invertible in the residue class ring K[X]/J. If the condition holds, J is shown to be the saturation ideal I:∞. We also show primary decompositions of the ideals I:∞ and I+9fm;:, where m is a natural number such that I:∞ = I:fm, all together forms a primary decomposition of I with no modification. These observations are especially useful for polynomial rings with parameters.
