A Morita type theorem for a sort of quotient categories

Simion Breaz

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 1, page 133-144
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

Breaz, Simion. "A Morita type theorem for a sort of quotient categories." Czechoslovak Mathematical Journal 55.1 (2005): 133-144. <http://eudml.org/doc/30932>.

@article{Breaz2005,
abstract = {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.},
author = {Breaz, Simion},
journal = {Czechoslovak Mathematical Journal},
keywords = {Morita theorem; quotient category; equivalent categories; adjoint functors; Morita theorems; quotient categories; equivalences of categories; adjoint functors; Serre classes},
language = {eng},
number = {1},
pages = {133-144},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A Morita type theorem for a sort of quotient categories},
url = {http://eudml.org/doc/30932},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Breaz, Simion
TI - A Morita type theorem for a sort of quotient categories
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 133
EP - 144
AB - 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.
LA - eng
KW - Morita theorem; quotient category; equivalent categories; adjoint functors; Morita theorems; quotient categories; equivalences of categories; adjoint functors; Serre classes
UR - http://eudml.org/doc/30932
ER -

References

top
  1. 10.1016/S0022-4049(00)00042-6, J.  Pure Appl. Algebra 158 (2001), 1–14. (2001) Zbl0983.20055MR1815779DOI10.1016/S0022-4049(00)00042-6
  2. 10.1216/rmjm/1181072651, Rocky Mountain J. Math. 22 (1992), 1227–1241. (1992) MR1201088DOI10.1216/rmjm/1181072651
  3. 10.1216/rmjm/1181072189, Rocky Mountain J. Math. 25 (1995), 827–842. (1995) MR1357094DOI10.1216/rmjm/1181072189
  4. Rings and Categories of Modules. Graduate Texts in Mathematics  13, Springer-Verlag, , 1973. (1973) MR1245487
  5. Finite Rank Torsion Free Abelian Groups and Rings. Lecture Notes in Mathematics Vol.  931, Springer-Verlag, , 1982. (1982) MR0665251
  6. 10.1023/A:1026255908301, Czechoslovak Math.  J. 53(128) (2003), 479–489. (2003) Zbl1027.16001MR1983467DOI10.1023/A:1026255908301
  7. On a quotient category, Studia Univ. Babeş-Bolyai Math. 47 (2002), 17–29. (2002) MR1989587
  8. Des catégories abelienes, Bull. Soc. Math. France 90 (1962), 323–448. (1962) MR0232821
  9. Theory of Categories, Editura Academiei, Bucureşti, 1979. (1979) 
  10. Rings of Quotients, Springer-Verlag, , 1975. (1975) MR0389953
  11. Torsion free abelian groups quasi-projective over their endomorphism rings II, Pac. J. Math. 74 (1978), 261–265. (1978) Zbl0349.20022MR0480777
  12. 10.2140/pjm.1977.68.527, Pacific J. Math. 68 (1977), 527–535. (1977) MR0480776DOI10.2140/pjm.1977.68.527
  13. Quotient categories and quasi-isomorphisms of abelian groups, In: Proc. Colloq. Abelian Groups, Budapest (1964), 1964, pp. 147–162. (1964) Zbl0142.26201MR0178069
  14. Foundations of Module and Ring Theory, Gordon and Breach, Reading, 1991. (1991) Zbl0746.16001MR1144522

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.