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拟polar环的注记(英文)

     

摘要

An element a in a ring R is called quasipolar if there exists p2 = p ∈ R such that p ∈comm2R(α), a+p E U(R) and ap E Rqnil; and a ring R is said to be quasipolax in case every element of R is quasipolar. In this note, we prove that any strongly π-regulax element in a ring R is quasipotar, and any quasipolar element in R is strongly clean. Several extension properties of quasipolar rings are also investigated.%称一个环R中的元素a是拟polar元,若存在p2=P∈R满足p∈comm_R~2(a),a+P∈U(R)并且ap∈R~(qnil);且称环R是拟polar的如果R中每一个元素都是拟polar元.本文证明了,任一环R中强π-正则元是拟polar的,而拟polar元是强clean的.拟polar环的一些扩张性质也作了探讨.

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