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arXiv · 2111.03475

Commutative bidifferential algebra

Omar Leon Sanchez·Rahim Moosa
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Abstract

Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with a {\em biderivation}, namely a binary operation that is a derivation in each argument, is here begun, with an eye toward the geometry of the corresponding {\em $B$-varieties}. Foundational results about extending biderivations to localisations, algebraic extensions and transcendental extensions are established. Resolving a deficiency in Poisson algebraic geometry, a theory of base extension is achieved, and it is shown that dominant $B$-morphisms admit generic $B$-fibres. A bidifferential version of the Dixmier-Moeglin equivalence problem is articulated.

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Omar Leon Sanchez, Rahim Moosa. 2021-11-05. Commutative bidifferential algebra. https://arxiv.org/abs/2111.03475

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