p. 137 - 144 Strong stably finite rings and some extensions
M. R. Vedadi Received: March 16, 2008;
Revised: September 17, 2008;
Accepted: September 22, 2008
Abstract.
A ring R is called right strong stably finite (r.ssf)
if for all n > 1, injective endomorphisms of R are
essential. If ^{n}_{R}R is an r.ssf ring and eR is an idempotent of R
such that eR is a retractable R-module, then eRe is an
r.ssf ring.
A direct product of rings is an r.ssf ring if and
only if each factor is so. R.ssf condition is investigated for
formal triangular matrix rings. In particular, if M is a
finitely generated module over a commutative ring R such that
for all n > 1, M^{(n)} is co-Hopfian, then
is an r.ssf ring. If _{R}X is a right denominator set of
regular elements of R, then R
is an r.ssf ring if and only if RX ^{–1} is so.
Keywords:
Co-Hopfian; Ore ring; strong stably finite; weakly co-Hopfian.
AMS Subject classification:
Primary: 16D10, 16D90
Secondary: 16P40, 16S10
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