论文标题
集体的平坦扩展和限制AI隔离的品种
Flat extensions of groups and limit varieties of ai-semirings
论文作者
论文摘要
本文是\ cite {jrz}的延续，并致力于研究添加性的半肢体的极限品种。极限品种是一种非绝对的品种，其适当的亚变量都是有限的。我们提出了一个无限的限制性家族的混凝土构造，并为添加性的半卵形品种和另一个临时例子。这些示例中的每个示例都可以通过有限的平面半段来生成，而无限族的族可以通过有限组的平坦扩展来产生的极限品种的完整表征产生。我们还展示了其他限制性型半肌的限制品种的示例，其中包括一个进一步的连续大小的家族，每个家族都没有有限的发电机，还有两个进一步的临时示例。虽然没有给出这些后一个示例的明确描述，但事实证明，其中一个仅包含琐碎的平坦半半。
The present paper is a continuation of \cite{jrz} and is devoted to the study of limit varieties of additively idempotent semirings. A limit variety is a nonfinitely based variety whose proper subvarieties are all finitely based. We present concrete constructions for one infinite family of limit additively idempotent semiring varieties, and one further ad hoc example. Each of these examples can be generated by a finite flat semiring, with the infinite family arising by a way of a complete characterisation of limit varieties that can be generated by the flat extension of a finite group. We also demonstrate the existence of other examples of limit varieties of additively idempotent semirings, including one further continuum-sized family, each with no finite generator, and two further ad hoc examples. While an explicit description of these latter examples is not given, one of the examples is proved to contain only trivial flat semirings.
