Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
Morita theorem; quotient category; equivalent categories; adjoint functors
Morita theorem; quotient category; equivalent categories; adjoint functors
Summary:
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.
References:
[1] U. Albrecht: Finite extensions of $A$-solvable abelian groups. J. Pure Appl. Algebra 158 (2001), 1–14. DOI 10.1016/S0022-4049(00)00042-6 | MR 1815779 | Zbl 0983.20055
[2] U. Albrecht: Quasi-decompositions of abelian groups and Baer’s Lemma. Rocky Mountain J. Math. 22 (1992), 1227–1241. DOI 10.1216/rmjm/1181072651 | MR 1201088
[3] U. Albrecht and P. Goeters: Almost flat abelian groups. Rocky Mountain J. Math. 25 (1995), 827–842. DOI 10.1216/rmjm/1181072189 | MR 1357094
[4] F. Anderson and K. Fuller: Rings and Categories of Modules. Graduate Texts in Mathematics 13. Springer-Verlag, , 1973. MR 1245487
[5] D. M. Arnold: Finite Rank Torsion Free Abelian Groups and Rings. Lecture Notes in Mathematics Vol. 931. Springer-Verlag, , 1982. MR 0665251
[6] S. Breaz: Almost-flat modules. Czechoslovak Math. J. 53(128) (2003), 479–489. DOI 10.1023/A:1026255908301 | MR 1983467 | Zbl 1027.16001
[7] S. Breaz and C. Modoi: On a quotient category. Studia Univ. Babeş-Bolyai Math. 47 (2002), 17–29. MR 1989587
[8] P. Gabriel: Des catégories abelienes. Bull. Soc. Math. France 90 (1962), 323–448. DOI 10.24033/bsmf.1583 | MR 0232821
[9] N. Popescu and L. Popescu: Theory of Categories. Editura Academiei, Bucureşti, 1979.
[10] B. Stenström: Rings of Quotients. Springer-Verlag, , 1975. MR 0389953
[11] C. Vinsonhaler: Torsion free abelian groups quasi-projective over their endomorphism rings II. Pac. J. Math. 74 (1978), 261–265. MR 0480777 | Zbl 0349.20022
[12] C. Vinsonhaler and W. Wickless: Torsion free abelian groups quasi-projective over their endomorphism rings. Pacific J. Math. 68 (1977), 527–535. DOI 10.2140/pjm.1977.68.527 | MR 0480776
[13] E. Walker: Quotient categories and quasi-isomorphisms of abelian groups. In: Proc. Colloq. Abelian Groups, Budapest (1964), 1964, pp. 147–162. MR 0178069 | Zbl 0142.26201
[14] R. Wisbauer: Foundations of Module and Ring Theory. Gordon and Breach, Reading, 1991. MR 1144522 | Zbl 0746.16001
Search
Partner of
