On right hereditary SPSD-rings of bounded representation type. Part 2

• Autorzy: Gubareni N.
• Języki publikacji: EN

Abstrakty

EN

In this paper right hereditary semiperfect semidistributive rings A = A(S,O) of bounded representation type are described in terms of Dynkin diagrams and diagrams with weights. We describe these rings using a reduction to mixed matrix problems over a discrete valuation ring and its skew field of fractions.

Słowa kluczowe

EN

right hereditary SPSD-rings; theory of rings

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2012
• Tom: Vol. 11, nr 4
• Strony: 53--63
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Gubareni N.

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

Bibliografia

• [1] Gabriel P., Indecomposable representations I, Manuscripta Math., 1972, 6, 71-103.
• [2] Nazarova L.A., Roiter A.V., Representations of partially ordered sets, Zap. Nauchn. Sem. LOMI 1972, 28, 5-31 (in Russian) (English transl.: J. Soviet Math. 1975, 3, 585-606).
• [3] Bernstein L.N., Gel'fand I.M., Ponomarev V.A., Coxeter functors and Gabriel's theorem, Uspekhi Math. Nauk, 1973, 28, 2(170), 19-33 (in Russian) (English translation: Russian Math. Survey 1973, 28, 2, 17-32).
• [4] Dlab V., Ringel C.M., On algebras of finite representation type, J. Algebra 1975, 33, 306-394.
• [5] Dlab V., Ringel C.M., Indecomposable representations of graphs and algebras, Memors Amer. Math. Soc., 1976, 173.
• [6] Dowbor P., Ringel C.M., Simson D., Hereditary Artinian rings of finite representation type, Lecture Notes in Math., vol. 832, Springer-Verlag 1980, 232-241.
• [7] Dowbor P., Simson D., A characterization of hereditary rings of finite representation type, Bull. Amer. Math. Soc. 1980, 2, 300-302.
• [8] Oppermann S., Auslander-Reiten Theory of Representation-Directed Artinian Rings, Ph.D. Thesis, University of Stuttgart 2005.
• [9] Gubareni N., Finitely presented modules over right hereditary SPSD-rings, Scientific Research of the Institute of Mathematics and Computer Science 2010, 2(9), 49-57.
• [10] Gubareni N., On right hereditary SPSD-rings of bounded representation type I, Scientific Research of the Institute of Mathematics and Computer Science 2012, 3(12).
• [11] Gubareni N., Structure of finitely generated modules over right hereditary SPSD-rings, Scientific Research of the Institute of Mathematics and Computer Science 2012, 3(12).
• [12] Dokuchaev M., Gubareni N., Rings connected with finite posets, Scientific Research of the Institute of Mathematics and Computer Science 2010, 2(9), 25-36.
• [13] Hazewinkel M., Gubareni N., Kirichenko V.V., Algebras, Rings and Modules. Vol. 2, Springer 2007.
• [14] Gubareni N.M., Right hereditary rings of bounded representation type, Preprint-148 Inst. Electrodynamics Akad. Nauk Ukrain. SSR, Kiev 1977, 48p (in Russian).