Baer and Baer *-ring characterizations of Leavitt path algebras |
| |
Authors: | Roozbeh Hazrat Lia Va? |
| |
Institution: | 1. Centre for Research in Mathematics, Western Sydney University, Australia;2. Department of Mathematics, Physics and Statistics, University of the Sciences, Philadelphia, PA 19104, USA |
| |
Abstract: | We characterize Leavitt path algebras which are Rickart, Baer, and Baer ?-rings in terms of the properties of the underlying graph. In order to treat non-unital Leavitt path algebras as well, we generalize these annihilator-related properties to locally unital rings and provide a more general characterizations of Leavitt path algebras which are locally Rickart, locally Baer, and locally Baer ?-rings. Leavitt path algebras are also graded rings and we formulate the graded versions of these annihilator-related properties and characterize Leavitt path algebras having those properties as well.Our characterizations provide a quick way to generate a wide variety of examples of rings. For example, creating a Baer and not a Baer ?-ring, a Rickart ?-ring which is not Baer, or a Baer and not a Rickart ?-ring, is straightforward using the graph-theoretic properties from our results. In addition, our characterizations showcase more properties which distinguish behavior of Leavitt path algebras from their -algebra counterparts. For example, while a graph -algebra is Baer (and a Baer ?-ring) if and only if the underlying graph is finite and acyclic, a Leavitt path algebra is Baer if and only if the graph is finite and no cycle has an exit, and it is a Baer ?-ring if and only if the graph is a finite disjoint union of graphs which are finite and acyclic or loops. |
| |
Keywords: | 16S10 16W10 16W50 16D70 |
本文献已被 ScienceDirect 等数据库收录! |
|