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SUMMARY:Elad Paran (The Open University of Israel\, Israel)
DTSTART:20260803T150000Z
DTEND:20260803T160000Z
DTSTAMP:20260825T033909Z
UID:ENAAS/187
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/187/">
 Algebraic geometry over division rings</a>\nby Elad Paran (The Open Univer
 sity of Israel\, Israel) as part of European Non-Associative Algebra Semin
 ar\n\n\nAbstract\nWe shall survey recent developments concerned with found
 ational aspects of algebraic geometry over division rings: \n\n \n\n1. A q
 uaternionic Nullstellensatz for the ring R of polynomials in n central var
 iables over the quaternion algebra H\, in both abstract form (due to the a
 uthor and Alon) and explicit form (due to M. Aryapoor).\n\n \n\n2. A theor
 em about the geometry of zero sets of polynomials in R: If a polynomial va
 nishes on all common zeros with commuting coordinates of a left ideal J in
  R \, then it vanishes on all common zeros of J in H^n. This result confir
 med a conjecture of Gori\, Sarfatti and Vlacci.\n\n \n\n3. Study of contra
 ction properties of one-sided ideals in polynomial rings over division rin
 gs. In particular\, we show that if M is a maximal left ideal in the polyn
 omial ring D[x]\, where D is a division ring\, then the contraction of M t
 o D need not be maximal. This resolved a question of Amitsur and Small fro
 m 1978. We shall discuss connections between this question to recent works
  and the implications to algebraic geometric over division rings. \n\n \n\
 nJoint works with Gil Alon\, Adam Chapman.\n
LOCATION:https://researchseminars.org/talk/ENAAS/187/
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