scholarly journals On the arithmetical rank of monomial ideals

1988 ◽  
Vol 112 (1) ◽  
pp. 86-89 ◽  
Author(s):  
Gennady Lyubeznik
Keyword(s):  
Monomial Ideals ◽  
Arithmetical Rank

On the Arithmetical Rank of the Edge Ideals of Some Graphs

2012 ◽  
Vol 19 (spec01) ◽  
pp. 797-806 ◽  
Author(s):  
Fatemeh Mohammadi ◽  
Dariush Kiani
Keyword(s):  
Projective Dimension ◽  
Monomial Ideals ◽  
Common Vertex ◽  
Edge Ideals ◽  
Arithmetical Rank

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.

scholarly journals Arithmetical rank of squarefree monomial ideals of small arithmetic degree

2008 ◽  
Vol 29 (3) ◽  
pp. 389-404 ◽  
Author(s):  
Kyouko Kimura ◽  
Naoki Terai ◽  
Ken-ichi Yoshida
Keyword(s):  
Monomial Ideals ◽  
Arithmetical Rank ◽  
Arithmetic Degree

scholarly journals A-graded methods for monomial ideals

2009 ◽  
Vol 322 (8) ◽  
pp. 2886-2904 ◽  
Author(s):  
Christine Berkesch ◽  
Laura Felicia Matusevich
Keyword(s):  
Monomial Ideals
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