Any semilocal Bezout ring is a~ring with elementary reduction of matrices (in Ukrainian) |
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| Author |
Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv
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| Abstract |
In this paper it is proved that any semilocal Bezout ring
is a ring with elmentary reduction of matrices. The conditions are found
under which any Hermitian ring is such a~ring. We give necessary and
sufficient conditions under which the class of quasi-euclidean rings
coincides with the~class of rings with elementary reduction of matrices.
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| Keywords |
semilocal Bezout ring, elementary reduction of matrices, Hermitian ring, quasi-euclidean rings
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| DOI |
doi:10.30970/ms.9.1.3-6
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Reference |
1. Cohn P. On the structure of the $GL_2$ of a ring I. H. E. S. Publ. Math. -- 1996. -- V.30. -- P.365--413.
2. Bougaut B. Anneaux Quasi-Euclidiens, Thése de docteur troisieme cycle. 1976. – 67p. 3. Kaplansky I. Elementary divisors and modules Trans. Amer. Math. Soc. – 1996. – V.166. – P.464–491. 4. Zabavsky B. Rings with elementary reduction of matrices. – Ring Theory Confer. Miskolc, Hungary, July 15–20, 1996. 5. Larsen M., Lewis W., Schores T. Elementary divisor rings and finitely presented modules Trans. Amer. Math. Soc. – 1974. – V.187. – P.231–248. 6. Забавский Б.В., Комарницкий Н.Я. Дистрибутивные области с элементарниыми делителями Укр. мат. журн. – 1990. – Т.42, №7. – С.1000–1004. 7. Naude C., Naude G., Brewer S.W. On Bezout domains elementary divisor rings and pole assignability Communs Algebra. – 1984. – V.12. – P.2987–3003. |
| Pages |
3-6
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| Volume |
9
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| Issue |
1
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| Year |
1998
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |