We prove some generalization of a lemma by Schmitt and Vogel which yields the arithmetical rank in cases that could not be settled by the existing methods. Our results are based on divisibility conditions and exploit both combinatorial and linear algebraic considerations. They mainly apply to ideals generated by monomials.
"Upper Bounds for the Arithmetical Ranks of Monomial Ideals." Tokyo J. Math. 35 (1) 23 - 34, June 2012. https://doi.org/10.3836/tjm/1342701342