On torsionfree classes which are not precover classes

Ladislav Bican

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 2, page 561-568
  • ISSN: 0011-4642

Abstract

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In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite type is presented.

How to cite

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Bican, Ladislav. "On torsionfree classes which are not precover classes." Czechoslovak Mathematical Journal 58.2 (2008): 561-568. <http://eudml.org/doc/31229>.

@article{Bican2008,
abstract = {In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite type is presented.},
author = {Bican, Ladislav},
journal = {Czechoslovak Mathematical Journal},
keywords = {hereditary torsion theory; exact; noetherian and perfect torsion theory; Goldie’s torsion theory; precover class; cover class; precover and cover of a module; hereditary torsion theories; exact torsion theories; Noetherian torsion theories; perfect torsion theories; Goldie torsion theory; precover classes; cover classes; torsionfree classes; categories of left modules; injective covers; relatively injective modules},
language = {eng},
number = {2},
pages = {561-568},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On torsionfree classes which are not precover classes},
url = {http://eudml.org/doc/31229},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Bican, Ladislav
TI - On torsionfree classes which are not precover classes
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 561
EP - 568
AB - In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite type is presented.
LA - eng
KW - hereditary torsion theory; exact; noetherian and perfect torsion theory; Goldie’s torsion theory; precover class; cover class; precover and cover of a module; hereditary torsion theories; exact torsion theories; Noetherian torsion theories; perfect torsion theories; Goldie torsion theory; precover classes; cover classes; torsionfree classes; categories of left modules; injective covers; relatively injective modules
UR - http://eudml.org/doc/31229
ER -

References

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