Some mixed matrix problems over several discrete valuation rings

• Autorzy: Gubareni N.
• Języki publikacji: EN

Abstrakty

EN

This article presents some results about several district valuation rings with a common skew field of fractions. They are obtained from the approximation theorem for discrete valuation rings. These results give the possibility to solve basic mixed matrix problems for such rings. We present the solution of some mixed flat matrix problems over several district valuation rings with common skew field of fractions.

Słowa kluczowe

EN

valuation rings; local invariant rings; discrete valuation rings; approximation theorem; mixed flat matrix problems

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2013
• Tom: Vol. 12, nr 4
• Strony: 47--58
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Gubareni N.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

• [1] Zavadskij A.G., Revitskaya U.S., A matrix problem over a discrete valuation rings, Mat. Sb. 1999, 190, 6, 835-858.
• [2] Zavadskij A.G., Kirichenko V.V., Torsion-free modules over primary rings, Zap. Nauchn. Sem. LOMI 1976, 57, 100-116 (in Rus.); English transl. in J. Soviet Math. 1979, 11.
• [3] Zavadskij A.G., Kirichenko V.V., Semimaximal rings of finite type, Mat. Sb. 1977, 103, 323-345.
• [4] Gubareni N.M., Semiperfect right hereditary rings of module representation type, Preprint 78.1, Academy of Sciences of USSR, IM, Kiev 1978 (in Rus.).
• [5] Kirichenko V.V., Kostyukovich P.P., Yaremenko Yu.V., Biserial rings and modules over these rings, Algebraic structures and their applications, Acadamy of Sciences of USSR, IM, Kiev 1988, 43-74 (in Rus.).
• [6] Hazewinkel M., Gubareni N., Kirichenko V.V., Algebras, Rings and Modules. Vol. 1, Kluwer Academic Publisher, 2004.
• [7] Hazewinkel M., Gubareni N., Kirichenko V.V., Algebras, Rings and Modules. Vol. 2, Springer, 2007.
• [8] Schilling O.F.G., Noncommutative valuations, Bull. Amer. Math. Soc. 1945, 51, 297-304.
• [9] Krull W., Allgemeine Bewertungstheorie, J. Reine Angew. Math. 1932, 167, 160-196.
• [10] Gubareni N., Valuation and discrete valuation rings, Scientific Research of the Institute of Mathematics and Computer Science 2011, 1(10), 61-70.
• [11] Brungs H.H., Gräter J., Noncommutative Prüfer and valuation rings, Comtemporary Mathematics, 1992, 131, Part 2, 253-269.
• [12] Gräter J., Lokalinvariant Bewertungen, Math. Z. 1986, 192, 183-194.
• [13] Brungs H.H., Gräter J., Valuation rings in finite-dimensional division algebras, J. Algebra 1989, 120, 90-99.
• [14] Mathiak K., Valuations of Skew Fields and Projective Hjelmslev Spaces, Springer-Verlag, 1986.