Testing flatness and computing rank of a module using syzygies

Oswaldo Lezama. "Testing flatness and computing rank of a module using syzygies." Colloquium Mathematicae 117.1 (2009): 65-79. <http://eudml.org/doc/284048>.

@article{OswaldoLezama2009,
abstract = {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.},
author = {Oswaldo Lezama},
journal = {Colloquium Mathematicae},
keywords = {Gröbner basis for defining ideal; monomial curve},
language = {eng},
number = {1},
pages = {65-79},
title = {Testing flatness and computing rank of a module using syzygies},
url = {http://eudml.org/doc/284048},
volume = {117},
year = {2009},
}

TY - JOUR
AU - Oswaldo Lezama
TI - Testing flatness and computing rank of a module using syzygies
JO - Colloquium Mathematicae
PY - 2009
VL - 117
IS - 1
SP - 65
EP - 79
AB - 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.
LA - eng
KW - Gröbner basis for defining ideal; monomial curve
UR - http://eudml.org/doc/284048
ER -