Higher-order Bernstein algebras given by symmetric bilinear forms

Towers, David and Bowman, Kevin (1997) Higher-order Bernstein algebras given by symmetric bilinear forms. Linear Algebra and its Applications, 252 (1-3). pp. 71-79. ISSN 0024-3795

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Abstract

Let (A, ω) be a kth-order Bernstein algebra and let N be the kernel of ω. This article studies the structure of such algebras in which N2 has dimension one. The algebras are of two types, I and II, according as N2 ⊆ U or N2 ⊈ U. A characterization of the algebras of type I is given. Power associative kth-order Bernstein algebras with dim N2 = 1 are then considered: they turn out to be Bernstein algebras of at most second order, and multiplication tables for these algebras over the real field are given. Finally, second-order Bernstein algebras of type II are examined and a structure theorem for them is obtained.

Item Type:
Journal Article
Journal or Publication Title:
Linear Algebra and its Applications
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2612
Subjects:
ID Code:
50003
Deposited By:
Deposited On:
28 Sep 2011 15:43
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Jan 2020 07:38