Geodesic
Strong stably finite rings and some extensions
Acta mathematica Universitatis Comenianae, Tome 78 (2009) no. 1 
M. R.  Vedadi. Strong stably  finite rings and some extensions. Acta mathematica Universitatis Comenianae, Tome 78 (2009) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2009_78_1_a14/
@article{AMUC_2009_78_1_a14,
     author = {M. R.  Vedadi},
     title = {Strong stably  finite rings and some extensions},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2009},
     volume = {78},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2009_78_1_a14/}
}
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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.