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

## 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: | Article |
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Journal or Publication Title: | Linear Algebra and its Applications |

Subjects: | |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 50003 |

Deposited By: | ep_importer_pure |

Deposited On: | 28 Sep 2011 16:43 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 21 Nov 2017 18:00 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/50003 |

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