The Value Semigroups of Prime Divisors of the Second Kind in 2-Dimensional Regular Local Rings

Valuation semigroups of two‐dimensional local rings

“…. , P r such that ν(W ) = ν(P k0 0 · · · P kr r ) for all K in the first sum of g in (41). We have that…”

The Poincaré series of a simple complete ideal of a two-dimensional regular local ring

“…[7], Corollary (2.2.1)). This semigroup was studied by Noh [8] and Spivakovsky [9] for k an algebraically closed field, and by Lipman [7] and Greco and…”

A class of projectively full ideals in two-dimensional Muhly local domains

“…Background information on Zariski's theory of complete ideals in 2-dimensional regular local rings can be obtained from [7], [11,Chapter 14] and [12]. Good references for briefly stated definitions and theorems from Zariski's theory of complete ideals are [9] and [10].…”

“…From the theory of complete ideals in a two-dimensional regular local ring (see for example[4,9,10]), we know that J is some power of the simple complete M -primary ideal that corresponds to w via Zariski's one-to-one correspondence. This unique simple complete M -primary ideal is the inverse transform of M s in R , where M s is as in the discussion at the end of Section 2 (cf [11,.…”