A Morita type theorem for a sort of quotient categories
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 133-144
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We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories.
We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories.
Classification : 16A50, 16B50, 16D90
Keywords: Morita theorem; quotient category; equivalent categories; adjoint functors
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Breaz, Simion. A Morita type theorem for a sort of quotient categories. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 1, pp. 133-144. http://geodesic.mathdoc.fr/item/CMJ_2005_55_1_a8/

[1] U.  Albrecht: Finite extensions of $A$-solvable abelian groups. J.  Pure Appl. Algebra 158 (2001), 1–14. | DOI | MR | Zbl

[2] U.  Albrecht: Quasi-decompositions of abelian groups and Baer’s Lemma. Rocky Mountain J. Math. 22 (1992), 1227–1241. | DOI | MR

[3] U. Albrecht and P. Goeters: Almost flat abelian groups. Rocky Mountain J. Math. 25 (1995), 827–842. | DOI | MR

[4] F.  Anderson and K. Fuller: Rings and Categories of Modules. Graduate Texts in Mathematics  13. Springer-Verlag, , 1973. | MR

[5] D. M.  Arnold: Finite Rank Torsion Free Abelian Groups and Rings. Lecture Notes in Mathematics Vol.  931. Springer-Verlag, , 1982. | MR

[6] S.  Breaz: Almost-flat modules. Czechoslovak Math.  J. 53(128) (2003), 479–489. | DOI | MR | Zbl

[7] S.  Breaz and C. Modoi: On a quotient category. Studia Univ. Babeş-Bolyai Math. 47 (2002), 17–29. | MR

[8] P.  Gabriel: Des catégories abelienes. Bull. Soc. Math. France 90 (1962), 323–448. | DOI | MR

[9] N.  Popescu and L.  Popescu: Theory of Categories. Editura Academiei, Bucureşti, 1979.

[10] B.  Stenström: Rings of Quotients. Springer-Verlag, , 1975. | MR

[11] C.  Vinsonhaler: Torsion free abelian groups quasi-projective over their endomorphism rings II. Pac. J. Math. 74 (1978), 261–265. | MR | Zbl

[12] C.  Vinsonhaler and W. Wickless: Torsion free abelian groups quasi-projective over their endomorphism rings. Pacific J. Math. 68 (1977), 527–535. | DOI | MR

[13] E.  Walker: Quotient categories and quasi-isomorphisms of abelian groups. In: Proc. Colloq. Abelian Groups, Budapest (1964), 1964, pp. 147–162. | MR | Zbl

[14] R.  Wisbauer: Foundations of Module and Ring Theory. Gordon and Breach, Reading, 1991. | MR | Zbl