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The FGF conjecture

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Pedro A. Guil Asensio, Universidad de Murcia

  • Algebra Seminar
When Thu, Oct 25, 2012
from 02:10 PM to 03:00 PM
Where Ritter Hall 134
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Abstract.  A ring is called right FGF (resp. right CF) if
every finitely generated (resp. cyclic) right module embeds
in a free module.  Two old conjectures by Faith state that
every right CF ring is right artinian, and every right FGF
ring is quasi-Frobenius.  In this talk, we will survey
some classical positive results on these conjectures and
we will discuss new advances which show the close relation between a solution of the conjecture and the behavior of the singular ideal of the ring.  We will also study the structure of right artinian, right CF rings, extending and completing previous characterizations obtained by S. K. Jain and S. R. L√≥pez-Permouth.

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