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Let $(R,\mathfrak{m})$ be a Noetherian local ring of characteristic $p>0$ . We introduce and study $F$ -full and $F$ -anti-nilpotent singularities, both are defined in terms of the Frobenius actions… Click to show full abstract
Let $(R,\mathfrak{m})$ be a Noetherian local ring of characteristic $p>0$ . We introduce and study $F$ -full and $F$ -anti-nilpotent singularities, both are defined in terms of the Frobenius actions on the local cohomology modules of $R$ supported at the maximal ideal. We prove that if $R/(x)$ is $F$ -full or $F$ -anti-nilpotent for a nonzero divisor $x\in R$ , then so is $R$ . We use these results to obtain new cases on the deformation of $F$ -injectivity.
Keywords:
frobenius actions;
local cohomology;
modules deformation;
cohomology modules;
actions local
Journal Title: Nagoya Mathematical Journal
Year Published: 2017
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Journal Title: Nagoya Mathematical Journal
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!