Let R be a ring graded by a finite group G. We study Quinn’s smash product R ˜#G * . We show that R is gr-regular if and only if R ˜#G * is regular. We also show that a homogeneous element of R has a homogeneous group inverse if and only if its corresponding element φ(r)∈R ˜#G * has a group inverse. A similar result is given for the Drazin inverse.
|Title of host publication||New techniques in Hopf algebras and graded ring theory. Selected papers of the congress|
|Editors||Stefaan Caenepeel, Fred Van Oystaeyen|
|Publication status||Published - 2007|
|Event||New techniques in Hopf algebras and graded ring theory - Brussel, Belgium|
Duration: Sept 19 2006 → …
|Conference||New techniques in Hopf algebras and graded ring theory|
|Period||9/19/06 → …|