A strong complement property of Dedekind domains

Abstract

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Elementary matrix reduction over certain rings

“…Furthermore, we generalize [9, Theorem 2.1] and prove that every J-stable ring is strongly completeable. This also extend [8,Theorem] to much wider class of rings (maybe with zero divisors).…”

“…Also every ring having almost stable range 1 is strongly completable. As a consequence, we have Corollary 4.14 [8,Theorem]. Every Dedekind domain is strongly completable.…”

Elementary matrix reduction over J-stable rings

“…Many known results are thereby generalized to much wider class of rings, e.g. [4,Theorem 14], [8,Theorem 3.7], [9,Theorem ], [11, Theorem 1.2.13 and Theorem 1.2.21] and [12,Theorem 32].…”

“…Thus, every VNL ring is strongly completable. As every Dedekind domain has almost stable range 1, it follows from Theorem 4.1 that every Dedekind domain is strongly completable[9, Theorem ].…”