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Preprint Number 2091
2091. Will Johnson Henselianity in NIP 𝔽_p-algebras E-mail: Submission date: 3 November 2021 Abstract: We prove an assortment of results on (commutative and unital) NIP rings, especially 𝔽_p-algebras. Let R be a NIP ring. Then every prime ideal or radical ideal of R is externally definable, and every localization S^{-1}R is NIP. Suppose R is additionally an 𝔽_p-algebra. Then R is a finite product of Henselian local rings. Suppose in addition that R is integral. Then R is a Henselian local domain, whose prime ideals are linearly ordered by inclusion. Suppose in addition that the residue field R/ℳ is infinite. Then the Artin-Schreier map R → R is surjective (generalizing the theorem of Kaplan, Scanlon, and Wagner for fields). Mathematics Subject Classification: 03C60 Keywords and phrases: |

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