域F_p上四维结合代数的同构分类

Classification of Associative Algebras of Dimension 4 Over Field F_p

给出了加群为初等 p群的 p4 阶有限结合环即域 Fp上四维结合代数的同构分类 ,选出了一个全体代表团 ,是为 p4 阶有限结合环的同构分类之三 ,方法是利用较低阶环的已知分类 ,并对非幂零情形籍助关于可离代数的 Wedderburn主定理与表示模理论 ,而对r=3的幂零情形还籍助于矩阵分类概念之发展 .

The finite associative rings of order p 4 with additive group of elementary type (p,p,p,p) are the associative algebras of dimension 4 over field F p. This paper gives their isomorphism classification and selects a complete set of representatives. This is the third part of the isomorphism classification of p 4 order finite associative rings.