An algorithm for primary decomposition in polynomial rings over the integers
نویسندگان
چکیده
منابع مشابه
An Algorithm for Primary Decomposition in Polynomial Rings over the Integers
We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and the idea of Shimoyama–Yokoyama resp. Eisenbud– Hunecke–Vasconcelos to extract primary ideals from pseudo–primary ideals. A parallelized version of the algor...
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We present an algorithm to compute the primary decomposition of a submodule N of the free module Z[x1, . . . , xn]. For this purpose we use algorithms for primary decomposition of ideals in the polynomial ring over the integers. The idea is to compute first the minimal associated primes of N , i.e. the minimal associated primes of the ideal Ann(Z[x1, . . . , xn]/N ) in Z[x1, . . . , xn] and the...
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We will reproduce a proof, using Hermann’s classical method, in Section 3 below. Note that the computable character of this bound reduces the question of whether f0 ∈ (f1, . . . , fn) for given fj ∈ F [X ] to solving an (enormous) system of linear equations over F . Hence, in this way one obtains a (naive) algorithm for solving the ideal membership problem for F [X ] (provided F is given in som...
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ژورنال
عنوان ژورنال: Central European Journal of Mathematics
سال: 2011
ISSN: 1895-1074,1644-3616
DOI: 10.2478/s11533-011-0037-8