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arXiv · 2311.15081

A Burnside ring for monoids

Jeremy Weissmann
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Abstract

In this note, we define the Burnside ring of a monoid, generalizing the construction for groups. After giving foundational definitions, we characterize transitive M-sets and their automorphisms, then prove a structure theorem for a broad class of monoids that allows us to write the Burnside ring as a direct product of Burnside rings of groups. Finally, we define a monoid correlate of the table of marks, and show that the Burnside algebra over the rationals is semisimple.

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BibTeXRIS

Jeremy Weissmann. 2023-11-25. A Burnside ring for monoids. https://doi.org/10.1016/j.jalgebra.2024.10.052

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