This article is cited in 4 papers

On algebras without proper subalgebras

V. A. Artamonov


Abstract: This paper deals with finite-dimensional algebras without proper subalgebras over a field. It is shown that if the dimension of such an algebra is a prime, then the automorphism group of the algebra is finite cyclic. Also described, under certain assumptions, are the algebras of prime dimension without subalgebras and with a nontrivial automorphism group.
Bibliography: 28 titles.

UDC: 519.4

MSC: 17A99

Received: 06.12.1976

 English version: Mathematics of the USSR-Sbornik, 1977, 33:3, 375–401

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