Rings related to finite posets

• Autorzy: Dokuchaev M. , Gubareni N.
• Języki publikacji: EN

Abstrakty

EN

In this article we consider special classes of rings related to finite partially ordered sets over division rings and prime hereditary Noetherian rings. The structure and main properties of these rings are studied. These rings are closely connected with right hereditary SPSD-rings.

Słowa kluczowe

EN

rings; posets

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
• Rocznik: 2010
• Tom: Vol. 9, nr 2
• Strony: 25--36
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Dokuchaev M.

autor

Gubareni N.

• Czestochowa University of Technology, Częstochowa, Poland,

Bibliografia

• [1] Rota G.-C., On the foundations of combinatorial theory I. Theory of Möbius functions, Z. Wahr Scheinlichkeits Therie und Verw. Gebiete, 2, 1964, 340-368.
• [2] Spiegel E., O'Donnell Ch.J., Incidence Algebras, Marcel Dekker, Inc., 1997.
• [3] Hazewinkel M., Gubareni N., Kirichenko V.V., Algebras, Rings and Modules, 1. Mathematics and Its Applications 575, Kluwer Academic Publisher 2004.
• [4] Hazewinkel M., Gubareni N., Kirichenko V.V., Algebras, rings and modules, 2. Springer 2007.
• [5] Warfield R.B., Jr., Bezout rings and serial rings, Comm. Algebra 1979, 7, 533-545.
• [6] Drozd Yu.A., The structure of hereditary rings, Math. Sbornik 1980, 113(155), (in Russian), English translation: Math. USSR Sbornik 1982, 41, 1, 139-148.
• [7] Gubareni N.M., Right hereditary rings of bounded representation type, Preprint-148 Inst. Electrodynamics Akad. Nauk Ukrain. SSR, Kiev 1977, (Russian).
• [8] Tuganbaev A.A., Distributive rings and modules, Trudy Moskov. Mat. Obshch. 1988, 51, 95-113.
• [9] Tuganbaev A.A., Semidistributive Modules and Rings, Kluwer Academic Press, 1998.
• [10] Kirichenko V.V., Mogileva V.V., Pirus E.M., Khibina M.A., Semiperfect rings and piecewise domains, [in:] Algebrai Researches, Institute of Mathematics NAS Ukraine 1995, 33-65.