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The finite basis problem for endomorphism semirings of finite chains
- Publication Year :
- 2023
-
Abstract
- For every semilattice $\mathcal{S}=(S,+)$, the set $\mathrm{End}(\mathcal{S})$ 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 $\mathrm{End}(\mathcal{S})$ where $\mathcal{S}$ is a finite chain.<br />Comment: 22 pages, 9 figures
- Subjects :
- Mathematics - Group Theory
16Y60, 08B05, 20M18
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2312.01770
- Document Type :
- Working Paper