• Degree and algebraic properties of lattice and matrix ideals 

      O'Carroll, Liam; Planas Vilanova, Francesc d'Assís; Villarreal Rodríguez, Rafael Heraclio (2014-01-01)
      Artículo
      Acceso abierto
      We 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 Herzog-Northcott type 

      Planas Vilanova, Francesc d'Assís; O'Carroll, Liam (2011-01-19)
      Artículo
      Acceso abierto
      This 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 (2018-03-02)
      Artículo
      Acceso abierto
      Based 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 (2015-06-01)
      Artículo
      Acceso abierto
      We 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 (2019-02-01)
      Artículo
      Acceso abierto
      Let 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 ...