论文标题
多项式身份较弱及其应用
Weak polynomial identities and their applications
论文作者
论文摘要
让$ r $为矢量子空间$ v $产生的字段$ k $的协会代数。自由关联代数的多项式$ f（x_1，\ ldots，x_n）$ $ k \ langle x_1，x_2，x_2，\ ldots \ rangle $是对$（r，v）$ n n $ r $在$ r $中消失在$ v $ v $ v $ v $时的弱$（r，v）。我们调查了弱的多项式身份及其对联想和接近非缔合代数的多项式身份和中心多项式的应用以及在有限的基础问题上。我们还提出了第三度多项式弱身份的结果。
Let $R$ be an associative algebra over a field $K$ generated by a vector subspace $V$. The polynomial $f(x_1,\ldots,x_n)$ of the free associative algebra $K\langle x_1,x_2,\ldots\rangle$ is a weak polynomial identity for the pair $(R,V)$ if it vanishes in $R$ when evaluated on $V$. We survey results on weak polynomial identities and on their applications to polynomial identities and central polynomials of associative and close to them nonassociative algebras and on the finite basis problem. We also present results on weak polynomial identities of degree three.
