Fractional skew monoid rings
| dc.creator | Ara, P. | |
| dc.creator | Gonzalez-Barroso, M. A. | |
| dc.creator | Goodearl, K. R. | |
| dc.creator | Pardo, E. | |
| dc.date | 2003-07-24 | |
| dc.date.accessioned | 2026-07-07T04:59:52Z | |
| dc.date.available | 2026-07-07T04:59:52Z | |
| dc.description | Given an action of a monoid $T$ on a ring $A$ by ring endomorphisms, and an Ore subset $S$ of $T$, a general construction of a fractional skew monoid ring $S^{\rm op} * A * T$ is given, extending the usual constructions of skew group rings and of skew semigroup rings. In case $S$ is a subsemigroup of a group $G$ such that $G=S^{-1}S$, we obtain a $G$-graded ring $S^{\rm op} * A * S$ with the property that, for each $s\in S$, the $s$-component contains a left invertible element and the $s^{-1}$-component contains a right invertible element. In the most basic case, where $G$ is the additive group of integers and $S=T$ is the submonoid of nonnegative integers, the construction is fully determined by a single ring endomorphism $α$ of $A$. If $α$ is an isomorphism onto a proper corner $pAp$, we obtain an analogue of the usual skew Laurent polynomial ring, denoted by $A[t_+,t_-;α]$. Examples of this construction are given, and it is proven that several classes of known algebras, including the Leavitt algebras of type $(1,n)$, can be presented in the form $A[t_+,t_-;α]$. Finally, mild and reasonably natural conditions are obtained under which $S^{\rm op} * A * S$ is a purely infinite simple ring. | |
| dc.identifier | https://arxiv.org/abs/math/0307320 | |
| dc.identifier | http://arxiv.org/abs/math/0307320 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68162 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16S35, 16S36; 16D30 | |
| dc.title | Fractional skew monoid rings | |
| dc.type | text |