A right Bezout ring with stable range 2, over which transpose matrix to invertible matrix is invertible, is the right Hermite ring (in Ukrainian)

Author I. V. Domsha

Ivan Franko National University of Lviv

Abstract It is proved that a right Bezout ring with stable range 2, over which transpose matrix to invertible matrix is invertible matrix, is the right Hermite ring.
Keywords Bezout ring with stable range 2; right Hermite ring
DOI
doi:10.30970/ms.36.1.31-33
Reference 1. Kaplansky I. Elementary divisors and modules// TAMS. – 1949. – V.66. – P. 464–491.

2. Larsen M., Lewis W., Shores T. Elementary divisor rings and finitelly presented modules// TAMS. – 1974. – V.187. – P. 231–248.

3. Zabavsky B.V. Fractionally regular Bezout rings// Mat. Stud. – 2009. – V.32, №1. – P. 76–80.

4. Bass H. K-theory and stable algebra// J. Hautes Etudes S. Publ. Math. – 1964. – V.22. – P. 485–544.

5. Забавський Б.В. Редукція матриць над кільцями Безу стабільного рангу не більше 2// Укр. мат. журнал - 2003. - Т.55. - №4. - С. 550-554.

6. Забавський Б.В. Редукція матриць над кільцями Безу стабільного рангу 2. - Третя між. алг. конф. в Україні, Суми, 2001.- 179с.

7. Cohn P.M. Unique factorization domains// Amer. Math. Monthly. – 1973. – V.80. – P. 1–17.

8. Vaserstein L.N. The stable rank of rings and dimensionality of topological spaces// Funct. Anal. Appl. – 1971. – V.5. – P. 102–110.

9. Gupta R.N., Khuran Anjana, Khuran Dinesh, Lam T.Y. Rings over which the transpose of every invertible matrix is invertible// J. Algebra – 2009. – V.322. – P. 1627–1636.

Pages 31-33
Volume 36
Issue 1
Year 2011
Journal Matematychni Studii
Full text of paper PDF
Table of content of issue HTML