游松发.素GPI-环的幂零多项式[J].数学研究及应用,2001,21(3):452~454 |
素GPI-环的幂零多项式 |
Nilpotent Polynomials of Prime GPI-Rings |
投稿时间:1998-06-15 |
DOI:10.3770/j.issn:1000-341X.2001.03.026 |
中文关键词: GPI-环 幂零 广义形心 基层 恒筹式 |
英文关键词:GPI-ring nilpotent extend centroid socle identity. |
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中文摘要: |
R是素GPI-环,若多项式f(x1,…,xd)在R上是幂零的,则或f(x1…,xd)是R的恒 等式,或R是有限域上的有限矩阵环 |
英文摘要: |
Assume that R is a prime GPI-ring. If a polynomial f(x1,...,xd) in the noncom muting variables x1, ...,xd and with the coefficients in the extended centroid C of R is nilpotent on R, then either f(x1, ...,xd) is a polynomial identity of R or R is a finite matrix ring over a finite field. |
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