Lance Bryant noticed in his thesis (Bryant, 2009 [3]), that there was a flaw in our paper (Barucci and Fröberg, 2006 [2]). It can be fixed by adding a condition, called the BF condition in Bryant (2009) [3]. We discuss some equivalent conditions, and show that they are fulfilled for some classes of rings, in particular for our motivating example of semigroup rings. Furthermore we discuss the connection to a similar result, stated in more generality, by Cortadellas and Zarzuela in [4]. Finally we use our result to conclude when a semigroup ring in embedding dimension at most three has an associated graded which is a complete intersection. © 2011 Elsevier Inc.
Associated graded rings of one-dimensional analytically irreducible rings II / Barucci, Valentina; Ralf, Froberg. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 336:1(2011), pp. 279-285. [10.1016/j.jalgebra.2010.12.033]
Associated graded rings of one-dimensional analytically irreducible rings II
BARUCCI, Valentina;
2011
Abstract
Lance Bryant noticed in his thesis (Bryant, 2009 [3]), that there was a flaw in our paper (Barucci and Fröberg, 2006 [2]). It can be fixed by adding a condition, called the BF condition in Bryant (2009) [3]. We discuss some equivalent conditions, and show that they are fulfilled for some classes of rings, in particular for our motivating example of semigroup rings. Furthermore we discuss the connection to a similar result, stated in more generality, by Cortadellas and Zarzuela in [4]. Finally we use our result to conclude when a semigroup ring in embedding dimension at most three has an associated graded which is a complete intersection. © 2011 Elsevier Inc.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
