On the arithmetical rank of the edge ideals of some graphs. (English) Zbl 1294.13030
Summary: In this paper, we compute the projective dimension of the edge ideals of graphs consisting of some cycles and lines which are joint in a common vertex. Moreover, we show that for such graphs, the arithmetical rank equals the projective dimension. As an application, we can compute the arithmetical rank for some homogenous monomial ideals.
MSC:
| 13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
| 13F55 | Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes |
| 13D05 | Homological dimension and commutative rings |
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