Abstract
Motivated by the Poisson Dixmier-Moeglin equivalence problem,
a systematic study of commutative unitary rings equipped with a biderivation,
namely a binary operation that is a derivation in each argument, is here begun,
with an eye toward the geometry of the corresponding B-varieties. Founda-
tional results about extending biderivations to localisations, algebraic exten-
sions and transcendental extensions are established. Resolving a deciency in
Poisson algebraic geometry, a theory of base extension is achieved, and it is
shown that dominant B-morphisms admit generic B-bres. A bidierential
version of the Dixmier-Moeglin equivalence problem is articulated.
a systematic study of commutative unitary rings equipped with a biderivation,
namely a binary operation that is a derivation in each argument, is here begun,
with an eye toward the geometry of the corresponding B-varieties. Founda-
tional results about extending biderivations to localisations, algebraic exten-
sions and transcendental extensions are established. Resolving a deciency in
Poisson algebraic geometry, a theory of base extension is achieved, and it is
shown that dominant B-morphisms admit generic B-bres. A bidierential
version of the Dixmier-Moeglin equivalence problem is articulated.
| Original language | English |
|---|---|
| Journal | Journal of Algebra |
| DOIs | |
| Publication status | Published - 4 Aug 2022 |