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The Nilpotent Regular Element Problem

  • Pere Ara (a1) and Kevin C. O'Meara (a2)


We use George Bergman's recent normal form for universally adjoining an inner inverse to show that, for general rings, a nilpotent regular element $x$ need not be unit-regular. This contrasts sharply with the situation for nilpotent regular elements in exchange rings (a large class of rings), and for general rings when all powers of the nilpotent element $x$ are regular.



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The Nilpotent Regular Element Problem

  • Pere Ara (a1) and Kevin C. O'Meara (a2)


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