|
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 |
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, ¹1. – P. 76–80.
4. Bass H. K-theory and stable algebra// J. Hautes Etudes S. Publ. Math. – 1964. – V.22. – P. 485–544.
5. Çàáàâñüêèé Á.Â. Ðåäóêö³ÿ ìàòðèöü íàä ê³ëüöÿìè Áåçó ñòàá³ëüíîãî ðàíãó íå á³ëüøå 2//
Óêð. ìàò. æóðíàë - 2003. - Ò.55. - ¹4. - Ñ. 550-554.
6. Çàáàâñüêèé Á.Â. Ðåäóêö³ÿ ìàòðèöü íàä ê³ëüöÿìè Áåçó ñòàá³ëüíîãî ðàíãó 2. -
Òðåòÿ ì³æ. àëã. êîíô. â Óêðà¿í³, Ñóìè, 2001.- 179ñ.
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.
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Pages |
31-33 |
Volume |
36 |
Issue |
1 |
Year |
2011 |
Journal |
Matematychni Studii |
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