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Mathematical logic, algebra and number theory

Addition to Block's theorem and to Popov's theorem on differentially simple algebras

V. N. Zhelyabin

Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia

Abstract: The paper gives examples of differentially simple algebras over the field of complex numbers, which are not represented in the form specified in Block's theorem. More precisely, examples of these algebras are finitely generated projective, but non-free, modules over their centroids. Recall, Popov's theorem states, that a differentially simple alternative non-associative algebra over a field of characteristic zero is a finitely generated projective module over the center.

Keywords: differentially simple algebra, projective module, associative algebra, alternative algebra, Jordan algebra, Lie algebra, Malcev algebra algebra of polynomials.

UDC: 512.554.7

MSC: 17C70

Received April 1, 2019, published October 7, 2019

DOI: 10.33048/semi.2019.16.095

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