ON DUO RINGS, PURE SEMISIMPLICITY AND FINITE REPRESENTATION TYPE

Authors
LARADJI A
Citation
A. Laradji, ON DUO RINGS, PURE SEMISIMPLICITY AND FINITE REPRESENTATION TYPE, Communications in algebra, 25(12), 1997, pp. 3947-3952
Citations number
13
Journal title
Communications in algebra → ACNP
ISSN journal
00927872
Volume
25
Issue
12
Year of publication
1997
Pages
3947 - 3952
Database
ISI
SICI code
0092-7872(1997)25:12<3947:ODRPSA>2.0.ZU;2-U
Abstract
In this note, we prove through a short and direct argument, that in le ft pure semisimple local rings, the two-sided ideals are principal. In particular, these rings are left (resp. right) uniserial if and only if they are left (resp. right) due. As a corollary we obtain that if a ring is a counter-example to the pure semisimple conjecture, then it cannot be a duo ring.