Details:
Title  Hilbert function of local Artinian level rings in codimension two  Author(s)  Valentina Bertella  Type  Article in Journal  Abstract  In this paper we characterize the possible Hilbert functions of a local Artinian level ring of given type and socle degree in the codimension two case. In particular, given an “admissible” numerical function h, an effective method is given to produce a zerodimensional ideal I of R = k 〚 x , y 〛 such that R / I is a local Artinian level ring having h as Hilbert function. As a consequence we recover the wellknown result proved by Briançon and Iarrobino concerning the Hilbert functions of a complete intersection of height two. We extend notions of standard or Gröbner bases from the graded to the local algebra context. The principal tools concern the concepts of enhanced standard basis and generic initial ideals which are defined for an ideal in the formal power series ring R = k 〚 x 1 , … , x n 〛 .  Keywords  Hilbert functions, Level local Artinian rings, Minimal number of generators, Monomial standard bases, Generic initial ideals  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869308005772 
Language  English  Journal  Journal of Algebra  Volume  321  Number  5  Pages  1429  1442  Year  2009  Edition  0  Translation 
No  Refereed 
No 
