Regular and Biregular module algebras
| dc.creator | Lomp, Christian | |
| dc.date | 2008-09-30 | |
| dc.date.accessioned | 2026-07-07T10:06:34Z | |
| dc.date.available | 2026-07-07T10:06:34Z | |
| dc.description | Motivated by the study of von Neumann regular skew groups as carried out by Alfaro, Ara and del Rio in 1995 we investigate regular and biregular Hopf module algebras. If $A$ is an algebra with an action by an affine Hopf algebra $H$, then any $H$-stable left ideal of $A$ is a direct summand if and only if $A^H$ is regular and the invariance functor $(-)^H$ induces an equivalence of $A^H$-Mod to the Wisbauer category of $A$ as $A# H$-module. Analogously we show a similar statement for the biregularity of $A$ relative to $H$ where $A^H$ is replaced by $R=Z(A)\cap A^H$ using the module theory of $A$ as a module over $A\otimes A^{op} \bowtie H$ the envelopping Hopf algebroid of $A$ and $H$. We show that every two-sided $H$-stable ideal of $A$ is generated by a central $H$-invariant idempotent if and only if $R$ is regular and $A_m$ is $H$-simple for all maximal ideals $m$ of $R$. Further sufficient conditions are given for $A# H$ and $A^H$ to be regular. | |
| dc.identifier | https://arxiv.org/abs/0810.0038 | |
| dc.identifier | http://arxiv.org/abs/0810.0038 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170372 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16N60 | |
| dc.title | Regular and Biregular module algebras | |
| dc.type | text |