On Flexible Algebras Satisfying x(yz) = y(zx)

被引：7

作者：

Behn, Antonio ^{[2
]}

Correa, Ivan ^{[1
]}

Hentzel, Irvin Roy ^{[3
]}

机构：

[1] Tokyo Metropolitana Cs Educ, Dept Matemat, Santiago, Chile

[2] Univ Chile, Fac Ciencias, Dept Matemat, Santiago, Chile

[3] Iowa State Univ, Dept Math, Ames, IA 50011 USA

来源：

ALGEBRA COLLOQUIUM | 2010年 / 17卷

关键词：

flexible; nilpotent; nil-algebra; semiprime;

D O I：

10.1142/S1005386710000829

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study flexible algebras (possibly infinite-dimensional) satisfying the polynomial identity x(yz) = y(zx). We prove that in these algebras, products of five elements are associative and commutative. As a consequence of this, we get that when such an algebra is a nil-algebra of bounded nil-index, it is nilpotent. Furthermore, we obtain optimal bounds for the index of nilpotency. Another consequence that we get is that these algebras are associative when they are semiprime.

引用

页码：881 / 886

页数：6

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