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SUMMARY:Nick Werner (SUNY Old Westbury)
DTSTART:20200430T200000Z
DTEND:20200430T210000Z
DTSTAMP:20260423T024652Z
UID:WMGAG/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WMGAG/2/">Co
 vering numbers of rings</a>\nby Nick Werner (SUNY Old Westbury) as part of
  GAG seminar\n\n\nAbstract\nA cover of a ring $R$ is a collection $C$ of p
 roper subrings of $R$ such that $R = \\bigcup_{S \\in C} S$. If such a col
 lection exists\, then $R$ is called coverable\, and the covering number of
  $R$ is the cardinality of the smallest possible cover. Questions that hav
 e been considered on this topic include determining covering numbers for c
 ertain families of rings\, or classifying all rings with a given covering 
 number. As we will demonstrate\, many of these questions can be reduced to
  the case of finite rings of characteristic $p$.\n\nThe analogous problem 
 of finding covering numbers of groups has been extensively studied. While 
 there are parallels between the group setting and the ring setting\, much 
 less is known in the case of rings. We will survey the known results on co
 vering numbers of rings\, and mention some conjectures and open problems\,
  among them the unresolved question of whether there exists a ring with co
 vering number 13.\n\nPassword to access the talk is the order of the symme
 tric group $S_9$.\n
LOCATION:https://researchseminars.org/talk/WMGAG/2/
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