Associated graded rings of one-dimensional analytically irreducible rings II

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.