This article is cited in 10 scientific papers (total in 10 papers)
Prime alternative algebras that are nearly commutative
S. V. Pchelintsev
We prove that by deforming the multiplication in a prime commutative alternative algebra using a C-operation we obtain a prime non-commutative alternative algebra. Under certain restrictions on non-commutative algebras this relation between algebras is reversible.
Isotopes are special cases of deformations. We introduce and study a linear space generated by the Bruck C-operations. We prove that the Bruck space is generated by operations of rank 1 and 2 and that “general” Bruck operations of rank 2 are independent in the following sense: a sum of $n$ operations of rank 2 cannot be written as a linear combination of
$(n-1)$ operations of rank 2 and an arbitrary operation of rank 1. We describe infinite series of non-isomorphic prime non-commutative algebras of bounded degree that are deformations of a concrete prime commutative algebra.
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Izvestiya: Mathematics, 2004, 68:1, 181–204
S. V. Pchelintsev, “Prime alternative algebras that are nearly commutative”, Izv. RAN. Ser. Mat., 68:1 (2004), 183–206; Izv. Math., 68:1 (2004), 181–204
Citation in format AMSBIB
\paper Prime alternative algebras that are nearly commutative
\jour Izv. RAN. Ser. Mat.
\jour Izv. Math.
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This publication is cited in the following articles:
S. V. Pchelintsev, “Structure of finitely generated commutative alternative algebras and special Moufang loops”, Math. Notes, 80:3 (2006), 396–402
S. V. Pchelintsev, “Exceptional prime alternative algebras”, Siberian Math. J., 48:6 (2007), 1060–1073
S. V. Pchelintsev, “Degenerate alternative algebras”, Siberian Math. J., 55:2 (2014), 323–335
A. S. Panasenko, “Just Infinite Alternative Algebras”, Math. Notes, 98:5 (2015), 805–812
S. V. Pchelintsev, “Isotopes of the alternative monster and the Skosyrsky algebra”, Siberian Math. J., 57:4 (2016), 666–678
V. N. Zhelyabin, A. S. Panasenko, “Nil Ideals of Finite Codimension in Alternative Noetherian Algebras”, Math. Notes, 101:3 (2017), 460–466
Pchelintsev S.V., “Proper identities of finitely generated commutative alternative algebras”, J. Algebra, 470 (2017), 425–440
S. V. Pchelintsev, O. V. Shashkov, “Simple $5$-dimensional right alternative superalgebras with trivial even part”, Siberian Math. J., 58:6 (2017), 1078–1089
S. V. Pchelintsev, “Prime algebras connected with monsters”, Siberian Math. J., 59:2 (2018), 341–356
V. N. Zhelyabin, A. S. Panasenko, “Nearly finite-dimensional Jordan algebras”, Algebra and Logic, 57:5 (2018), 336–352
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