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A Property of Unit Regular Rings

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Dan Bossaller, Saint Louis University

What
  • Algebra Seminar
When Thu, Nov 08, 2012
from 02:10 PM to 03:00 PM
Where Ritter Hall 134
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Abstract. A ring  R  is called unit regular if for each element
a  of  R  there exists a unit  u  such that  aua = a.  A ring
is called clean if any element can be written as the sum of a unit and an idempotent.  In this talk I will present a proof by Victor Camillo and Dinesh Khurana that a ring is unit regular if and only if for any  a  in  R  there exist a unit  u and an idempotent  e  in  R  such that  a = e+u  and  aR ∩ eR = 0.

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