## Gröbner bases and primary decomposition of polynomial ideals.(English)Zbl 0667.13008

An algorithm to compute the primary decomposition of ideals in a polynomial ring over a “factorially closed algorithmic principal ideal domain” (see the paper for the technical definition) is given. The construction is based on the Gröbner basis algorithm. Induction over the dimension is used and localization at principal primes lowers the dimension. In the zero-dimensional case Gröbner bases are again used for decomposing. Finally it is showed how the reduction process can be applied to computing radicals and testing for primality.
Reviewer: R.Fröberg

### MSC:

 13F20 Polynomial rings and ideals; rings of integer-valued polynomials 13-04 Software, source code, etc. for problems pertaining to commutative algebra 68W30 Symbolic computation and algebraic computation 13A15 Ideals and multiplicative ideal theory in commutative rings
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### References:

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