Strong Stably Finite Rings and Some Extensions
نویسنده
چکیده
A ring R is called right strong stably finite (r.ssf) if for all n ≥ 1, injective endomorphisms of R (n) R are essential. If R is an r.ssf ring and e 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. The 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 R is co-Hopfian, then h EndR(M) M 0 R i 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.
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