This article is cited in 4 papers

Just Infinite Alternative Algebras

A. S. Panasenko<sup>ab

a</sup> Novosibirsk State University
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: Alternative just infinite-dimensional algebras are studied, i.e., infinite-dimensional algebras in which every nonzero ideal has finite codimension. It is proved that these algebras are prime. In the nonassociative case, the Noetherian property with respect to one-sided ideals is proved, and the cases of Cayley–Dickson rings and exceptional algebras are investigated.

Keywords: alternative algebra, just infinite-dimensional algebra, prime algebra, Noetherian property with respect to one-sided ideals, Cayley–Dickson ring, exceptional algebra.

UDC: 512.554.5

MSC: 17D05

Received: 06.03.2015

DOI: 10.4213/mzm10709

 English version: Mathematical Notes, 2015, 98:5, 805–812

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