Abstract:
The primary decomposition methods of Eisenbud, Huneke and Vasconcelos are anal-
ysed in detail providing proofs of important theorems and all the corresponding al-
gorithms are programmed in the language of Singular. MOreover, we investigated
the parallelization of two modular algorithms. In fact, we consider the modular com-
putation of Gr ̈obner bases (resp. standard bases) and the modular computation of
the associated primes of a zero–dimensional ideal and describe their parallel imple-
mentation in Singular. The algorithms of Shimoyama and Yokoyama for primary
decomposition of ideals are generalized to submodules of a free module over the
polynomial ring in several variables with coefficients in a field. The algorithms are
implemented in Singular.
