The finite basis problem for endomorphism semirings of finite chains

2023/12/04 by Gusev, Sergey V., Volkov, Mikhail V. · 1 citation
#08B05 #16Y60 #20M18 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2312.01770

Abstract

For every semilattice S=(S,+), the set End(S) of its endomorphisms forms a semiring under point-wise addition and composition. We prove that the semiring of all endomorphisms of the 3-element chain has no finite identity basis. This, combined with earlier results by Dolinka (The finite basis problem for endomorphism semirings of finite semilattices with zero, Algebra Universalis 61, 441-448 (2009)), gives a complete solution to the finite basis problem for semirings of the form End(S) where S is a finite chain.

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• The finite basis problem for the endomorphism semirings of finite semilattices

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