A counterpart to Nagata idealization

作者：Olberding Bruce^*

来源：Journal of Algebra, 2012, 365: 199-221.

DOI：10.1016/j.jalgebra.2012.05.002

• Idealization
• Trivialization
• Noetherian ring
• Cohen-Macaulay ring

Idealization of a module K over a commutative ring S produces a ring having K as an ideal, all of whose elements are nilpotent. We develop a method that under suitable field-theoretic conditions produces from an S-module K a subring R of S that behaves like the idealization of K but is such that when S is a domain, so is R. The ring S is contained in the normalization of R but is finite over R only when R = S. We determine conditions under which R is Noetherian, Cohen-Macaulay, Gorenstein, a complete intersection or a hypersurface. When R is local, then its m-adic completion is the idealization of the m-adic completions of S and K.

• 出版日期2012-9-1