Congruence-simplicity of Steinberg algebras of non-Hausdorff ample groupoids over semifields |
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| Institution: | 1. Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Viet Nam;2. Faculty of Computer Science and Mathematics, University of Passau, Germany;1. University of Missouri-Columbia, Mathematics Department, Columbia, MO, USA;2. College of the Ozarks, Mathematics Department, Point Lookout, MO, USA;1. The Ohio State University at Lima, Lima, OH, USA;2. Università di Camerino, Camerino, Italy;1. Department of Mathematics, Chung-Ang University, Seoul 06974, Republic of Korea;2. Department of Mathematics Education, Chosun University, Gwangju 61452, Republic of Korea;1. Department of Mathematics, Faculty of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810 Japan;2. Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810 Japan |
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| Abstract: | We investigate the algebra of an ample groupoid, introduced by Steinberg, over a semifield S. In particular, we obtain a complete characterization of congruence-simpleness for Steinberg algebras of second-countable ample groupoids, extending the well-known characterizations when S is a field. We apply our congruence-simplicity results to tight groupoids of inverse semigroup representations associated to self-similar graphs. |
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| Keywords: | Étale groupoids Ample groupoids Congruence-simple semirings Steinberg algebras |
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