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SUMMARY:Philipp Rothmaler (CUNY)
DTSTART:20211005T190000Z
DTEND:20211005T200000Z
DTSTAMP:20260423T004658Z
UID:PALS/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PALS/13/">Hi
 gh and low formulas</a>\nby Philipp Rothmaler (CUNY) as part of PALS Pangl
 obal Algebra and Logic Seminar\n\n\nAbstract\nA partition of the set of un
 ary positive primitive (pp) formulas for modules over an associative ring 
 into four regions will be presented. These four types of formula have a be
 aring on various structural properties of modules\, a few instances of whi
 ch will be discussed in the talk. Domains\, specifically Ore domains\, tur
 n out to play a prominent role.\n\nOne of the four types of formula are ca
 lled high. These are used to define Ulm submodules and Ulm length of modul
 es over an arbitrary associative ring. Pure injective modules turn out to 
 have Ulm length at most 1 (just as in abelian groups). As a consequence\, 
 pure injective modules over RD domains (in particular\, pure injective mod
 ules over the first Weyl algebra over a field of characteristic 0) decompo
 se into a largest injective and a reduced submodule.\n
LOCATION:https://researchseminars.org/talk/PALS/13/
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