Geodesic
Testing flatness and computing rank of a module using syzygies
Oswaldo Lezama1
1 Departamento de Matemáticas Universidad Nacional de Colombia Bogotá, Colombia
Colloquium Mathematicum, Tome 117 (2009) no. 1, pp. 65-79 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

Using syzygies computed via Gröbner bases techniques, we present algorithms for testing some homological properties for submodules of the free module $A^m$, where $A=R[x_1,\dots,x_n]$ 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.
DOI : 10.4064/cm117-1-4
Keywords: using syzygies computed via bner bases techniques present algorithms testing homological properties submodules module where dots noetherian commutative ring test given submodule flat check locally constant dimension moreover present algorithm computes rank flat submodule algorithm computes projective dimension arbitrary submodule algorithms illustrated examples

Oswaldo Lezama 1

1 Departamento de Matemáticas Universidad Nacional de Colombia Bogotá, Colombia 
@article{10_4064_cm117_1_4,
     author = {Oswaldo Lezama},
     title = {Testing flatness and computing rank of a
 module using syzygies},
     journal = {Colloquium Mathematicum},
     pages = {65--79},
     year = {2009},
     volume = {117},
     number = {1},
     doi = {10.4064/cm117-1-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm117-1-4/}
}
TY  - JOUR
AU  - Oswaldo Lezama
TI  - Testing flatness and computing rank of a
 module using syzygies
JO  - Colloquium Mathematicum
PY  - 2009
SP  - 65
EP  - 79
VL  - 117
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm117-1-4/
DO  - 10.4064/cm117-1-4
LA  - en
ID  - 10_4064_cm117_1_4
ER  - 
%0 Journal Article
%A Oswaldo Lezama
%T Testing flatness and computing rank of a
 module using syzygies
%J Colloquium Mathematicum
%D 2009
%P 65-79
%V 117
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/cm117-1-4/
%R 10.4064/cm117-1-4
%G en
%F 10_4064_cm117_1_4
Oswaldo Lezama. Testing flatness and computing rank of a
 module using syzygies. Colloquium Mathematicum, Tome 117 (2009) no. 1, pp. 65-79. doi: 10.4064/cm117-1-4

Cité par Sources :