Graded quasi-Baer $\ast$-ring characterization of Steinberg algebras

Morteza Ahmadi; Ahmad Moussavi

Graded quasi-Baer $\ast$-ring characterization of Steinberg algebras

Rings and Algebras 2024-05-07 v1

Authors: Morteza Ahmadi , Ahmad Moussavi

Abstract

Given a graded ample, Hausdorff groupoid $G$ , and an involutive field $K$ , we consider the Steinberg algebra $A_K(G)$ . We obtain necessary and sufficient conditions on $G$ under which the annihilator of any graded ideal of $A_K(G)$ is generated by a homogeneous projection. This property is called graded quasi-Baer $\ast$ . We use the Steinberg algebra model to characterize graded quasi-Baer $\ast$ Leavitt path algebras.

Keywords

Steinberg algebra graded ideal quasi-Baer Leavitt path algebra homogeneous projection

Cite

@article{arxiv.2405.02997,
  title  = {Graded quasi-Baer $\ast$-ring characterization of Steinberg algebras},
  author = {Morteza Ahmadi and Ahmad Moussavi},
  journal= {arXiv preprint arXiv:2405.02997},
  year   = {2024}
}

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