Semihereditary rings and related topics

• Autorzy: Gubareni N.
• Języki publikacji: EN

Abstrakty

EN

A ring A is called right (left) semihereditary if all finitely generated right (left) ideals of A are projective. In this paper we consider non-commutative semihereditary rings and show their connection with non-commutative valuation rings. We also present some criterion for a module to be flat.

Słowa kluczowe

EN

semihereditary rings; homological algebra; non commutative rings

PL

pierścienie półdziedziczne; algebra homologiczna; pierścienie nieprzemienne

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2011
• Tom: Vol. 16
• Strony: 33--38
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Gubareni N.

• Institute of Mathematics Częstochowa University of Technology Dąbrowskiego 73, 42-200 Częstochowa, Poland

Bibliografia

• [1] H. Cartan, S. Eilenberg. Homological Algebra. Princeton University Press, Princeton, New York 1956.
• [2] S.U. Chase. Direct products of modules. Trans. Amer. Math. Soc., 97, 457-473, 1960.
• [3] N.I. Dubrovin. Noncommutative valuation rings. Trudy Moskov. Obshch., 45, 265-280, 1982. (In Russian). English transl.: Trans. Moscow Math. Soc., 45, 273-287, 1984.
• [4] M. Hazewinkel, N. Gubareni, V.V. Kirichenko. Algebras, Rings and Modules. Vol. 1, Mathematics and Its Applications, vol. 575, Kluwer Academic Publisher, Dordrecht 2004.
• [5] H. Marubayashi, H. Mijamoto, A. Ulda. Non-commutative Valuation Rings and Semi-hereditary Orders. Kluwer Academic Publisher, Dordrecht 1997.
• [6] O.F.G. Schilling. Noncommutative valuations. Bull. Amer. Math. Soc., 51, 297-304, 1945.
• [7] R.B. Warfield, Jr. Serial rings and finitely presented modules. J. Algebra, 37, No. 2, 187-222, 1975.