Rings whose modules are finitely generated over their endomorphism rings

Nguyen Viet Dung, and José Luis García. "Rings whose modules are finitely generated over their endomorphism rings." Colloquium Mathematicae 114.2 (2009): 155-176. <http://eudml.org/doc/286151>.

@article{NguyenVietDung2009,
abstract = {A module M is called finendo (cofinendo) if M is finitely generated (respectively, finitely cogenerated) over its endomorphism ring. It is proved that if R is any hereditary ring, then the following conditions are equivalent: (a) Every right R-module is finendo; (b) Every left R-module is cofinendo; (c) R is left pure semisimple and every finitely generated indecomposable left R-module is cofinendo; (d) R is left pure semisimple and every finitely generated indecomposable left R-module is finendo; (e) R is of finite representation type. Moreover, if R is an arbitrary ring, then (a) ⇒ (b) ⇔ (c), and any ring R satisfying (c) has a right Morita duality.},
author = {Nguyen Viet Dung, José Luis García},
journal = {Colloquium Mathematicae},
keywords = {endofinite modules; right pure semisimple rings; rings of finite representation type; pure semisimplicity conjecture; direct sums of finitely generated modules; finendo modules; cofinendo modules; local dualities},
language = {eng},
number = {2},
pages = {155-176},
title = {Rings whose modules are finitely generated over their endomorphism rings},
url = {http://eudml.org/doc/286151},
volume = {114},
year = {2009},
}

TY - JOUR
AU - Nguyen Viet Dung
AU - José Luis García
TI - Rings whose modules are finitely generated over their endomorphism rings
JO - Colloquium Mathematicae
PY - 2009
VL - 114
IS - 2
SP - 155
EP - 176
AB - A module M is called finendo (cofinendo) if M is finitely generated (respectively, finitely cogenerated) over its endomorphism ring. It is proved that if R is any hereditary ring, then the following conditions are equivalent: (a) Every right R-module is finendo; (b) Every left R-module is cofinendo; (c) R is left pure semisimple and every finitely generated indecomposable left R-module is cofinendo; (d) R is left pure semisimple and every finitely generated indecomposable left R-module is finendo; (e) R is of finite representation type. Moreover, if R is an arbitrary ring, then (a) ⇒ (b) ⇔ (c), and any ring R satisfying (c) has a right Morita duality.
LA - eng
KW - endofinite modules; right pure semisimple rings; rings of finite representation type; pure semisimplicity conjecture; direct sums of finitely generated modules; finendo modules; cofinendo modules; local dualities
UR - http://eudml.org/doc/286151
ER -