Monomial ideals of linear type

Let S=K[x1,…,xn;y1,…,ym] be the polynomial ring in 2 sets of variables over a field K. We investigate some classes of monomial ideals of S in order to classify ideals of the linear type.

Monomial ideals of linear type

Let S=K[x1,…,xn;y1,…,ym] be the polynomial ring in 2 sets of variables over a field K. We investigate some classes of monomial ideals of S in order to classify ideals of the linear type.

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  • Bruns, W., Herzog, J.: Cohen–Macaulay Rings (Cambridge Studies in Advanced Mathematics 39) Cambridge. Cambridge University Press 1993.
  • Conca, A., De Negri, E.: M -sequences, graph ideal and ladder ideals of linear type. J. Alg. 211, 599–624 (1999). Herzog, J., Restuccia, G., Tang, T.: s -Sequences and symmetric algebras. Manuscripta Math. 104, 479–501 (2001). Huneke, C.: On the symmetric and Rees algebra of an ideal generated by a d-sequence. J. Alg. 62, 268–275 (1980). La Barbiera, M.: Normalization of Veronese bi-type ideals. Ital. J. Pure Appl. Math. 26, 79–92 (2009).
  • La Barbiera, M.: On a class of monomial ideals generated by s-sequences. Math. Reports 12, 201–216 (2010).
  • La Barbiera, M.: A note on unmixed ideals of Veronese bi-type. Turk. J. Math. 37, 1–7, (2013).
  • La Barbiera, M., Restuccia, G.: Mixed product ideals generated by s-sequences. Alg. Colloq. 18, 553–570 (2011). La Barbiera, M., Staglian` o, P.L.: Generalized graph ideals of linear type. In press.
  • Restuccia, G., Villarreal, R.H.: On the normality of monomial ideals of mixed products. Comm. Alg. 29, 3571–3580 (2001).
  • Sturmfels, B.: Groebner Bases and Convex Polytopes. Providence, RI, USA. American Mathematical Society 1991. Valla, G.: On the symmetric and Rees algebra of an ideal. Manuscripta Math. 30, 239–255 (1980).
  • Villarreal, R.H.: Monomial Algebras (Pure and Appl. Math. 238). New York. Marcel Dekker 2001.