Semiprime FDI-rings

• Autorzy: Gubareni N.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present some results for FDI-rings, i.e. rings with a complete set of pairwise orthogonal primitive idempotents. We consider the nilpotency index of ideals and give its upper band for ideals in some classes of rings. We also give a new proof of a criterion of semiprime FDI-rings to be prime.

Słowa kluczowe

EN

semiprime rings; prime rings; nilpotent ideal; nilpotency index; Jacobson radical; semiperfect ring; complete set of idempotents; FDI-rings

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 4
• Strony: 49--59
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Gubareni N.

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

Bibliografia

• [1] Dokuchaev M.A., Gubareni N.M., Kirichenko V.V., Rings with finite decomposition of identity, Ukrain. Mat. Zh. 2011, 63(3), 319-340.
• [2] Kirichenko V.V., Khibina M.A., Semiperfect semidistributive rings, [in:] Infinite Groups and Related Algebraic Structures, Acad. Nauk Ukrainy, Inst. Mat., Kiev 1993, 457-480 (in Russian).
• [3] Drozd Yu.A., The structure of hereditary rings, Math. Sbornik 1980, 113(155), 1(9), 161-172 (in Russian); English translation: Math. USSR Sbornik 1982, 41(1), 139-148.
• [4] Gordon R., Small L.W., Piecewise domains, Journal of Algebra 1972, 23, 553-564.
• [5] Rowen L.H., Ring Theory, Vol. 1, Acad. Press, New York-Boston 1988.
• [6] Hazewinkel M., Gubareni N., Kirichenko V.V., Algebras, Rings and Modules, Vol. 1, Kluwer Academic Publisher, 2004.
• [7] Bass H., Finistic dimension and homological generalization of semiprimary rings, Trans. Amer. Math. Soc. 95, 1960, 466-488.
• [8] Müller B., On semiperfect rings, Ill. J. Math. 1970, 14, 3, 464-467.
• [9] Birkenmeier G.F., Heatherly H.E., Kim J.Y., Triangular matrix representations, Journal of Algebra 2000, 230, 558-595.