PreprintarXiv licencearXiv
Equational theories of flat semirings S(W)
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).
Related
BibTeX
@misc{gao2026equational,
title = {{Equational theories of flat semirings $S(W)$}},
author = {Zidong Gao and Yilin Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20308},
eprint = {2610.20308},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20308},
}
RIS
TY - UNPB
TI - Equational theories of flat semirings S(W)
AU - Zidong Gao
AU - Yilin Zhou
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20308
UR - https://arxiv.org/abs/2610.20308
AB - 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).
ER -