Vol. LXXVIII, 1 (2009)
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 RnR are essential. If 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)R is co-Hopfian, then is an r.ssf ring. If 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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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

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