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SUMMARY:Pace Nielsen (Brigham Young University\, USA)
DTSTART:20220315T160000Z
DTEND:20220315T170000Z
DTSTAMP:20260423T021433Z
UID:ONCAS/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ONCAS/15/">N
 ilpotent polynomials with non-nilpotent coefficients</a>\nby Pace Nielsen 
 (Brigham Young University\, USA) as part of ONCAS Online Noncommutative Al
 gebra Seminar\n\n\nAbstract\nIt is well known that the coefficients of nil
 potent polynomials over noncommutative rings generally are not all nilpote
 nt.  We show that this remains true even under extremely strong restrictio
 ns on the set of nilpotents in the coefficient ring.  If $R$ is a ring and
  its set of nilpotents\, ${\\rm Nil}(R)$\, satisfies ${\\rm Nil}(R)^2=0$\,
  then in general ${\\rm Nil}(R[x])\\not \\subseteq {\\rm Nil}(R)[x]$.  Thi
 s is proven by constructing an explicit polynomial example.  The smallest 
 possible degree of such a polynomial is seven.  Related problems are raise
 d\, as well as connections to Kothe's conjecture and work of Agata Smoktun
 owicz.\n
LOCATION:https://researchseminars.org/talk/ONCAS/15/
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