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arxiv: 2507.03709 · v3 · pith:5TIYC4NXnew · submitted 2025-07-04 · 🧮 math.RA

Counting finite semirings

classification 🧮 math.RA
keywords finiteisomorphismsemiringssmallanti-isomorphismcountcountingexisting
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In this short note we count the finite semirings up to isomorphism, and up to isomorphism or anti-isomorphism for some small values of $n$; for which we utilise the existing library of small semigroups in the GAP package Smallsemi.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A new limit variety of additively idempotent semirings

    math.RA 2026-03 unverdicted novelty 7.0

    SR_6 generates a limit variety V(SR_6) with a four-element chain subvariety lattice, establishing it as nonfinitely based while all proper subvarieties are finitely based.