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Testing flatness and computing rank of a module using syzygies

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Lezama O.

Colloquium Mathematicum

2009

tom 117

nr 1

65-79

Using syzygies computed via Gröbner bases techniques, we present algorithms for testing some homological properties for submodules of the free module $A^{m}$, where A = R[x₁,...,xₙ] and R is a Noetherian commutative ring. We will test if a given submodule M of $A^{m}$ is flat. We will also check if M is locally free of constant dimension. Moreover, we present an algorithm that computes the rank of a flat submodule M of $A^{m}$ and also an algorithm that computes the projective dimension of an arbitrary submodule of $A^{m}$. All algorithms are illustrated with examples.

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1 Colloquium Mathematicum

1 Lezama O.

1 2009

Wyniki wyszukiwania

Testing flatness and computing rank of a module using syzygies