Year: 2026
Type: preprint
Abstract: For positive integers \(m,n\), let \[ A_{m,n}=(\{1,\ldots,m\}\times\Z_n)\cup\{0\} \] have flat addition and multiplication truncated at degree \(m\). We prove that \(A_{m,n}\) is finitely based exactly when \(m\le 2\) or \((m,n)=(3,1)\). Explicit finite bases are supplied throughout this region. Outside it, high-girth hypergraphs with a constant-sum rigidity property yield finite countermodels to every bounded-variable fragment of the equational theory. The proof places no divisibility or coprimality restriction on the parameters.
Source: arXiv (Cornell University)
Authors: Ma, Qirui, Gao, Zidong
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214073407