Euclidean full matrices.
Keywords:
full matrix, elementary divisor ring, Euclidean ring, euclidean ring, principal ideal domainsAbstract
This paper shows that over commutative rings elementary divisors of an arbitrary set of full matrix order n is 2- Euclidean set. Over arbitrary principal ideal domain full set of matrices of order 2 set is Euclidean, and the order n is 2- Euclidean set.References
Jacobson N. Basic Algebra 1 / N. Jacobson. – W. H. Freeman and Company, 1985.
Jacobson N. Ring theory. / N. Jacobson. – M.: Izdatelsvo inostrannoy literatury, 1947.
Kaplansky I. Elementary divisors and modules / I. Kaplansky // Trans. Amer. Math. Soc. – 1949. – V. 166. – P. 464- 491.
Samuel P. About Euclidean rings / P. Samuel // Journal of Algebra. – 1971. – V. 19. – P. 282-301.
P. Lezowski. On some Euclidean properties of matrix algebras [Electronic resourse] / Pierre Lezowski // Electronic data. – [Talence, 2015]. – Mode of access: https://hal.inria.fr/hal-01135202v2/document (viewed on July 10, 2016).
Забавський Б.В. Стабільний ранг множини повних матриць над кільцем елементарних дільників / Б.В. Забавський, Б.М. Кузніцька // Укр. мат. журнал. – 2014. – Т. 66, № 5. – с. 697-700.
