Testing flatness and computing rank of a module using syzygies

• Autorzy: Oswaldo Lezama
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 13D02: Syzygies, resolutions, complexes
• 13D05: Homological dimension
• 13P10: Gr\"obner bases; other bases for ideals and modules (e.g., Janet and border bases)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 117
• Numer: 1
• Strony: 65-79

Daty

wydano

2009

Twórcy

autor

Oswaldo Lezama

• Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia

Identyfikatory

DOI

10.4064/cm117-1-4