Commutative bidifferential algebra
Commutative Algebra
2021-11-08 v1 Logic
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 -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 -morphisms admit generic -fibres. A bidifferential version of the Dixmier-Moeglin equivalence problem is articulated.
Cite
@article{arxiv.2111.03475,
title = {Commutative bidifferential algebra},
author = {Omar Leon Sanchez and Rahim Moosa},
journal= {arXiv preprint arXiv:2111.03475},
year = {2021}
}