Browsing by Author "O'Carroll, Liam"
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Degree and algebraic properties of lattice and matrix ideals
O'Carroll, Liam; Planas Vilanova, Francesc d'Assís; Villarreal Rodríguez, Rafael Heraclio (20140101)
Article
Open AccessWe study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give formulas to compute the degree in terms of the torsion of certain factor groups of Z(s) and in terms of relative volumes of lattice ... 
Ideals of HerzogNorthcott type
Planas Vilanova, Francesc d'Assís; O'Carroll, Liam (20110119)
Article
Open AccessThis paper takes a new look at ideals generated by 2×2 minors of 2×3 matrices whose entries are powers of three elements not necessarily forming a regular sequence. A special case of this is the ideals determining monomial ... 
Minimal free resolutions of lattice ideals of digraphs
O'Carroll, Liam; Planas Vilanova, Francesc d'Assís (20180302)
Article
Open AccessBased upon a previous work of Manjunath and Sturmfels for a finite, complete, undirected graph, and a refined algorithm by Eröcal, Motsak, Schreyer and Steenpaß for computing syzygies, we display a free resolution of the ... 
Noncomplete intersection prime ideals in dimension 3
Goto, Shiro; O'Carroll, Liam; Planas Vilanova, Francesc d'Assís (20150601)
Article
Open AccessWe describe prime ideals of height 2 minimally generated by three elements in a Gorenstein, Nagata local ring of Krull dimension 3 and multiplicity at most 3. This subject is related to a conjecture of Y. Shimoda and to a ... 
On the integral degree of integral ring extensions
Giral Silió, José María; O'Carroll, Liam; Planas Vilanova, Francesc d'Assís; Plans Berenguer, Bernat (20190201)
Article
Open AccessLet A ¿ B be an integral ring extension of integral domains with fields of fractions K and L, respectively. The integral degree of A ¿ B, denoted by dA(B), is defined as the supremum of the degrees of minimal integral ...