2016
DOI: 10.1016/j.laa.2016.06.034
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Some matrix completions over integral domains

Abstract: We characterize 3×3 nilpotent matrices which are completions of 2×2 arbitrary matrices and 3 × 3 idempotent matrices which are completions of 2 × 2 arbitrary matrices over integral domains. As an application we show that a nil-clean element of a ring which belongs to a corner of the ring, may not be nil-clean in this corner.

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