约当代数的长度及以后

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-06-16 DOI:10.1016/j.jalgebra.2025.05.030

A.E. Guterman , D.K. Kudryavtsev

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引用次数: 0

摘要

证明了特征不同于2的域上的交换约当代数的长度由上面的维数有界。这个界与关联代数的界相同，但我们证明了给定的关联代数的长度可以大于、小于或等于对应的伴随约当代数的长度。我们还证明了Jordan恒等式本身（甚至在特征2中具有交换性）并不能保证生长的线性界。此外，我们还计算了双复数和双四元数的精确长度。

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The length of Jordan algebras and beyond

We prove that the length of the commutative Jordan algebras over a field of the characteristic different from 2 is bounded by the dimension from above. This bound is the same as for the class of associative algebras, but we demonstrate that the length of a given associative algebra can be either greater or lesser or equal to the length of the corresponding adjoint Jordan algebra. We also show that the Jordan identity by itself (or even with commutativity in characteristic 2) does not guarantee a linear bound on growth. In addition, we compute the exact length of bicomplex numbers and biquaternions.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.