Associated graded rings of one-dimensional analytically irreducible rings II

作者：Barucci Valentina; Froberg Ralf^*

来源：Journal of Algebra, 2011, 336(1): 279-285.

DOI：10.1016/j.jalgebra.2010.12.033

• One-dimensional ring
• Associated graded ring
• Analytically irreducible

Lance Bryant noticed in his thesis (Bryant, 2009 [3]), that there was a flaw in our paper (Barucci and Froberg, 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.

• 出版日期2011-6-15