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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2014 Volume 55, Number 2, Pages 396–411 (Mi smj2542)

This article is cited in 8 papers

Degenerate alternative algebras

S. V. Pchelintsevab

a Finance Academy of the Government of the Russian Federation, Moscow, Russia
b Moscow City Pedagogical University, Moscow, Russia

Abstract: We prove that each degenerate alternative algebra of characteristic $\ne2$ contains a nonzero ideal with an additive basis consisting of the absolute zero divisors of an arbitrary large order. As a corollary we establish the existence of infinitely many nonisomorphic commutative prime alternative algebras and existence of infinite series of strict and nonstrict exceptional alternative algebras with different sets of proper identities.

Keywords: alternative algebra, absolute zero divisor of an arbitrary order, exceptional prime algebra, C-operation, identity, alternative monster, isotope.

UDC: 512.554.5

Received: 15.08.2013


 English version:
Siberian Mathematical Journal, 2014, 55:2, 323–335

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© Steklov Math. Inst. of RAS, 2025