包含与所有幂等元交换的非零幂等元的四维绝对值代数

IF 0.5 2区数学 Q3 MATHEMATICS

International Journal of Algebra and Computation Pub Date : 2023-01-01 DOI:10.12988/ija.2023.91757

A. Moutassim, Mohamed Mohamed Louzari, Aziz Es. Sadiq

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引用次数: 0

摘要

在[9]中，我们证明了如果A是一个四维绝对值代数，它有两个不同的子代数同构于C，则A同构于H、m1、m2或m3。在这里我们完成了对A的研究。事实上，我们证明了A是否有两个不同的子代数与* C同构。则A同构于∗H，∗m1，∗m2或∗m3。进一步，我们分类了所有四维绝对值代数，其中包含一个非零幂等交换与所有幂等交换，这样的代数a包含至少两个不同的子代数同构于∗C。这意味着A同构于∗H，∗m1，∗m2或∗m3。

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Four dimensional absolute valued algebras containing a nonzero idempotent commuting with all idempotents

In [9], we have proven that if A is a four-dimensional absolute valued algebra having two diﬀerent subalgebras isomorphic to C , then A is isomorphic to H , M 1 , M 2 or M 3 . Here we complete the study of A . Indeed, we show if A has two diﬀerent subalgebras isomorphic to ∗ C . Then A is isomorphic to ∗ H , ∗ M 1 , ∗ M 2 or ∗ M 3 . Furthermore, we classify all four-dimensional absolute valued algebras containing a nonzero idempotent commuting with all idempotents, such an algebra A contains at least two diﬀerent subalgebras isomorphic to ∗ C . Which means that A is isomorphic to ∗ H , ∗ M 1 , ∗ M 2 or ∗ M 3 .

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来源期刊

International Journal of Algebra and Computation 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.