The coordinate ring of an \(n\)-dimensional sphere and some examples of differentially simple algebras. (English. Russian original) Zbl 1387.17006
Algebra Logic 52, No. 4, 277-289 (2013); translation from Algebra Logika 52, No. 4, 416-434 (2013).
Summary: Using the coordinate ring of an \(n\)-dimensional real sphere, we construct examples of differentially simple algebras which are finitely generated projective, but nonfree, modules over their centroids. As a consequence, examples of such algebras are obtained in varieties of associative, Lie, alternative, Mal’tsev, and Jordan algebras.
MSC:
| 17A36 | Automorphisms, derivations, other operators (nonassociative rings and algebras) |
| 12H05 | Differential algebra |
| 13N15 | Derivations and commutative rings |
Keywords:
differentially simple algebra; module; centroid; variety; Lie algebra; alternative algebra; Mal’tsev algebra; Jordan algebraReferences:
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