The finite basis problem for the endomorphism semirings of finite semilattices

2025/08/02 by Dolinka, Igor, Gusev, Sergey V., Volkov, Mikhail V.
#08B05 #16Y60 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.01212

Abstract

For every semilattice A=(A,+), the set End(A) of its endomorphisms forms a semiring under pointwise addition and composition. We prove that that if A is finite, then the endomorphism semiring End(A) has a finite identity basis if and only if |A|≤ 2.

Citations

• The finite basis problem for endomorphism semirings of finite chains
• Nonfinitely based ai-semirings with finitely based semigroup reducts
• Semiring identities of the Brandt monoid

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