OU- OSU Ring Theory Seminar
A kernel functor defined by relative injectivity, and its application to some rings, by Noyan Er (University of Rio Grande, Rio Grande) .
May 03, 2013
from 05:45 PM to 06:45 PM
|Where||MW 154 (OSU-Columbus.)|
|Contact Name||Sergio R. Lopez-Permouth|
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Abstract: Let M and N be two modules and i_M(N) stand for the largest submodule of N relative to
which M is injective. i_M thus defines a left exact preradical on Mod-R, and i_M(M) is quasi-injective.
This functor is used to characterize classes of rings including strongly prime, QI, semiartinian rings
and those with no middle class: A ring R is semisimple or right strongly prime <=> for any right
R-module M, i_M(R)=R or 0, extending a result of Rubin; R is right QI <=> it has a.c.c. on essential
right ideals and i_M is a radical for each M in Mod-R (a.c.c. is not redundant), extending a partial
answer of Dauns and Zhou to a long standing open problem;
R is right semiartinian <=> the only radicals of the form i_M are those with M injective.
Radicals that can be expressed in the form i_M for some module M are completely determined:
Such a radical is precisely the largest left exact preradical vanishing at a module with zero socle.