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- W2951440872 abstract "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 $K$ and derivation $D:Srightarrow K$ 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 ${bf m}$-adic completion is the idealization of the ${bf m}$-adic completions of $S$ and $K$." @default.
- W2951440872 created "2019-06-27" @default.
- W2951440872 creator A5084698513 @default.
- W2951440872 date "2012-04-18" @default.
- W2951440872 modified "2023-09-27" @default.
- W2951440872 title "A counterpart to Nagata idealization" @default.
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