id: 01570908 dt: j an: 01570908 au: Laubenbacher, Reinhard; Schlauch, Karen ti: An algorithm for the Quillen-Suslin theorem for quotients of polnomial rings by monomial ideals. so: J. Symb. Comput. 30, No.5, 555-571 (2000). py: 2000 pu: Elsevier Science (Academic Press), London la: EN cc: ut: monomial ideal; free module; Gröbner basis; square-free; Quillen-Suslin theorem; Stanley-Reisner ring ci: li: doi:10.1006/jsco.2000.0367 ab: The Quillen-Suslin theorem states the following. Consider a $m\times m$-matrix $M$ with polynomial entries from $k[x].$ The columns generate a submodule $P$ of $k[x]^m.$ If $P$ is projective then the submodule $\ker(M)$ has a free basis. The authors generalize this result to the case that $k[x]$ is replaced by the quotient ring $k[x]/I$ where I is a monomial ideal. An algorithm for the construction of a free basis of ker(M) is presented. The first step is the redution to the square-free case. Ideas of Vorst are used to represent the square-free quotient ring as a pullback of two quotient rings. The construction uses a Stanley-Reisner ring of a simplicial complex. This idea of two rings is repeated until polynomial rings are found. Here the original Quillen-Suslin theorem can be used and the algorithm works backward to reconstruct the free basis of the original $\ker(M)$. The lifting algorithm involves Gröbner bases. The last section illustrates the algorithm by an example. This paper will be interesting to people working in commutative algebra and computational algebra. rv: Karin Gatermann (Berlin)