Kazimirsky's rings

О.V.Domsha; B.V.Zabavsky

In this paper the notion of the Kazimirsky ring as generalization of 2-simple Ore domain with stable range 1 is introduced. Matrices which are not zero divisors are considered. Block-diagonal reduction of these matrices over Kazimirsky domain that is Ore domain is shown.

1. Bass X. K-theory and stable algebra// J. Hauntes Etudes Scien. Publ. Math. -- 1964. -- V.22. -- P. 485--544.

2. Забавський Б.В. Простые кольца элементарных делителей// Мат. Cтуд. -- 2004. -- Т.22, №2. -- С.~129--133.

3. Olszewski J. On ideals of product of rings// Demons. Math., Poland. -- 1994. -- V.27, №1. -- P. 1--7.

4. Казімірський П. С. Нормальна форма матриці над кільцем $L$// Вісн. Львів. політехн. ін-ту. -- 1970. -- T.44. -- С. 3--13.

5. Кон П. Свободные кольца и их связи. -- М.: Мир., 1974.

	Kazimirsky's rings (in Ukrainian)
Author	О.V.Domsha, B.V.Zabavsky Ivan Franko National University of Lviv, Department of Mechanics and Mathematics
Abstract	In this paper the notion of the Kazimirsky ring as generalization of 2-simple Ore domain with stable range 1 is introduced. Matrices which are not zero divisors are considered. Block-diagonal reduction of these matrices over Kazimirsky domain that is Ore domain is shown.
Keywords	Kazimirsky ring, Ore domain, zero divisor, block-diagonal reduction
DOI	doi:10.30970/ms.34.1.75-79
Reference	1. Bass X. K-theory and stable algebra// J. Hauntes Etudes Scien. Publ. Math. -- 1964. -- V.22. -- P. 485--544. 2. Забавський Б.В. Простые кольца элементарных делителей// Мат. Cтуд. -- 2004. -- Т.22, №2. -- С.~129--133. 3. Olszewski J. On ideals of product of rings// Demons. Math., Poland. -- 1994. -- V.27, №1. -- P. 1--7. 4. Казімірський П. С. Нормальна форма матриці над кільцем $L$// Вісн. Львів. політехн. ін-ту. -- 1970. -- T.44. -- С. 3--13. 5. Кон П. Свободные кольца и их связи. -- М.: Мир., 1974.
Pages	75-79
Volume	34
Issue	1
Year	2010
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Kazimirsky's rings (in Ukrainian)