Using syzygies computed via Gröbner bases techniques, we present algorithms for testing some homological properties for submodules of the free module , where A = R[x₁,...,xₙ] and R is a Noetherian commutative ring. We will test if a given submodule M of 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 and also an algorithm that computes the projective dimension of an arbitrary submodule of . All algorithms are illustrated with examples.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-4,
author = {Oswaldo Lezama},
title = {Testing flatness and computing rank of a module using syzygies},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {65-79},
zbl = {1181.13027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-4}
}
Oswaldo Lezama. Testing flatness and computing rank of a module using syzygies. Colloquium Mathematicae, Tome 116 (2009) pp. 65-79. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-4/