Reducing the matrices to the canonical diagonal form by invertible toeplitz matrices.
Keywords:
тoeplitz matrix, unit square stable range one, square stable range one, properties of matricesAbstract
This paper shows that commutative rings elementary divisors square stable range one, an arbitrary matrix of the second order is reduced to canonical diagonal form invertible Toeplitz matrices. Also we established the properties of Toeplitz matrices.References
Bass H. K-theory and stable algebra / H. Bass // Publ. Math. IHES. – 1964. – V. 22. – P. 5-60 p.
Ara P. Strongly π-regular rings have stable range 1 / P. Ara // Proc. Amer. Math. Soc. – 1996. – V. 124. – P. 3293- 3298.
Camillo V. Stable Range 1 for rings with many idempotens / V. Camillo, H.-P. Yu // Trans. Amer. Math. Soc. – 1995. – V. 347. – P. 3141-3147.
Estes D. Stable range in commutative rings / D. Estes, J. Ohm // J. Algebra. – 1967. – V 7. – P. 343−362.
Vaserstein I. N. Bass`s first stable range condition / I.N. Vaserstein // J. Pure Appl. Algebra. – 1984. – V. 34. – P. 319-330.
Zabavsky B.V. Diagonal reduction of matrices over rings / B.V Zabavsky // Math. Studies. – Lviv, 2012. – V. 16. – 251 p.
Zabavsky B.V. Diagonal reduction of matrices over finite stable range rings / B.V. Zabavsky // Math. Studies Monograph Series. – 2014. – V. 41, № 1. – P. 101-108.
Khurana D. Rings of square stable rang one / D. Khurana, T.Y. Lam, Zhou Wang // J. Algebra. – 2011. – V. 338. – P. 122-143.
Zabavsky B. V. Distributive elementary divisor domains / Zabavsky B.V., Komarnytsry M.Y. // Ukr. Math. J. 1996. – V. 42, № 7. – P. 890-892.
