Year: 2026
Type: preprint
Abstract: We study the finite basis problem for flat semirings of the form $S(W)$, where $W$ is a nonempty set of nonempty words, possibly infinite. We prove that $S(W)$ is finitely based if and only if the strict interior of every word in $W$ is linear; here the strict interior of a word is obtained by deleting its first and last letters. This completely resolves an open problem raised by Jackson et al.~(J. Algebra 611: 211--245, 2022).
Source: arXiv (Cornell University)
Authors: Gao, Zidong, Zhou, Yilin
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221995599