OU-OSU Ring Theory Seminar
A note on aleph_0-injective rings, by Liang Shen (Southeast University, Nanjing, China and Ohio University Center of Ring Theory and its Applications)
| What |
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|---|---|
| When |
Oct 16, 2009 from 04:45 pm to 05:45 pm |
| Where | MW 154 (Columbus campus of Ohio State University) |
| Contact Name | Sergio Lopez-Permouth |
| Contact Email | lopez@ohio.edu |
| Contact Phone | 740-590-0527 |
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Abstract: A ring R is called right aleph_0-injective if every right homomorphism
from a countably generated right ideal of R to R_{R} can be extended to a
homomorphism from R_{R} to R_{R}. In this note, some characterizations
of aleph_0-injective rings are given. It is proved that if R is semiperfect,
then R is right aleph_0-injective if and only if every homomorphism from
a countably generated small right ideal of R to R_{R} can be extended to
one from R_{R} to R_{R}. It is also shown that if R is right noetherian
and left aleph_0-injective, then R is \emph{QF}. This result can be
looked as an approach to the Faith-Menal conjecture.
