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Baer and Baer *-ring characterizations o...
Hazrat, Roozbeh...

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Baer and Baer *-ring characterizations of Leavitt path algebras by Hazrat, Roozbeh ( Author )
Lemonjar Open Access
N.A
17-06-2016
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 C∗-algebra counterparts. For example, while a graph C∗-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.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1606.05692
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