Abstract
As a continuation of the study of the Steinberg algebra of a Hausdorff ample groupoid \({\mathcal {G}}\) over commutative semirings by Nam et al. (J. Pure Appl. Algebra 225, 2021), we consider here the Steinberg algebra \(A_S({\mathcal {G}})\) with coefficients in a Clifford semifield S. We obtain a complete characterization of the full k-ideal simplicity of \(A_S({\mathcal {G}})\). Using this result for the Steinberg algebra \(A_S({\mathcal {G}}_\Gamma )\) of the graph groupoid \({\mathcal {G}}_\Gamma \), where \(\Gamma \) is a row-finite digraph and S is a Clifford semifield, we characterize the full k-simplicity of the Leavitt path algebra \(L_S(\Gamma )\).
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Acknowledgements
The authors convey their sincere gratitude to (retd.) Prof. M.K. Sen of University of Calcutta for his continuous encouragement. The authors are very much grateful to the learned referee for his careful reading of the manuscript and subsequent valuable suggestions which have helped a lot to improve the quality of the paper. Finally the first author likes to thank University Grants Commission (UGC) for providing Junior Research Fellowship (ID: 211610022010/Joint CSIR-UGC NET JUNE 2021).
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Mukherjee, P., Sardar, S.K. Full k-simplicity of Steinberg algebras over Clifford semifields with application to Leavitt path algebras. Arch. Math. 122, 501–512 (2024). https://doi.org/10.1007/s00013-024-01975-1
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DOI: https://doi.org/10.1007/s00013-024-01975-1