发表机构
School of Mathematics, Northwest University（西北大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了特定Brandt半环无有界变量数的恒等式基，给出平坦群扩张的有限基准则，还涉及逆半环分类等相关结果。
AI 中文摘要
我们证明，具有至少两个指标的非平凡群上的Brandt半环不存在变量数有界的恒等式基。一组均匀的有限见证大小与变量界呈线性关系，适用于任意基数的群。通过交换构造得到了指数无界的群的平坦扩张的对应结果，并给出了任意平坦群扩张的精确有限基准则。结构表示导出了有限自然逆半环的分类，以及正则半环中刻画局部Clifford自然逆结构的单一恒等式。我们还描述了乘积、正交和、最小生成元、着色图恒等式和线性变量复杂性。进一步的结果涉及无限生成代数和固有的非有限可基性。
英文摘要
We prove that Brandt semirings over nontrivial groups with at least two indices admit no identity basis with a bounded number of variables. A uniform family of finite witnesses has size linear in the variable bound and applies to groups of arbitrary cardinality. A commutative construction yields the corresponding result for flat extensions of groups of unbounded exponent and gives an exact finite basis criterion for arbitrary flat group extensions. Structural representations lead to a classification of finite natural inverse semirings and a single identity characterizing locally Clifford natural inverse structure among regular semirings. We also describe products, orthogonal sums, minimum generators, colored graph identities and linear variable complexity. Further results concern infinite generating algebras and inherent nonfinite basability.
