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  • LINQUAN MA (a1) and PHAM HUNG QUY (a2)

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.

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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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