EUCLIDEAN DOMAINS AND SKEW LAURENT FORMAL SERIES RINGS

EUCLIDEAN DOMAINS AND SKEW LAURENT FORMAL SERIES RINGS

It is proved that if R is a right [omega]-Euclidean domain, then a formal skew Laurent power series ring is a right [omega]-Euclidean domain. It is shown that if R is a right [omega]-Euclidean domain with multiplicative norm, then a skew Laurent formal power series ring is a right principal ideal do...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-11, Vol.277 (1), p.47
Hauptverfasser: Romaniv, O.M, Sagan, A.V
Format: Artikel
Sprache:eng
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Zusammenfassung:It is proved that if R is a right [omega]-Euclidean domain, then a formal skew Laurent power series ring is a right [omega]-Euclidean domain. It is shown that if R is a right [omega]-Euclidean domain with multiplicative norm, then a skew Laurent formal power series ring is a right principal ideal domain. We also prove that if R is a noncommutative [omega]-Euclidean domain with multiplicative norm, then a skew Laurent formal power series ring is a ring with elementary reduction of matrices.
ISSN:1072-3374
DOI:10.1007/s10958-023-06812-4