一些无爱音节变体

Pub Date : 2024-02-14 DOI:10.1007/s00233-024-10411-3

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引用次数: 0

摘要

摘要我们研究了一些 nil-ai-semiring varieties。我们为所有交换平半音生成的 \(\textbf{FC}\) 中的自由客体建立了一个模型。同时，我们还提供了有限ai-semiring是非无限基础的两个充分条件。因此，我们证明了有限 nil semigroup \({\dot{S}}_{c}(W)}\) 的 power semiring \(P_{\scriptstyle {\dot{S}}_{c}(W)}\) 是非无限基于的、其中，W 是字母表 X 上自由交换半群 \(X_{c}^{+}\)中单词的有限集合，只要 W 中单词长度的最大值是 \(k\ge 3\)，并且 W 不包含字母的第 k 次幂。这部分回答了杰克逊等人提出的一个问题（J Algebr 611: 211-245, 2022）。

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Some nil-ai-semiring varieties

Abstract

We study some nil-ai-semiring varieties. We establish a model for the free object in the variety \(\textbf{FC}\) generated by all commutative flat semirings. Also, we provide two sufficient conditions under which a finite ai-semiring is nonfinitely based. As a consequence, we show that the power semiring \(P_{\scriptstyle {\dot{S}}_{c}(W)}\) of the finite nil-semigroup \({\dot{S}}_{c}(W)\) is nonfinitely based, where W is a finite set of words in the free commutative semigroup \(X_{c}^{+}\) over an alphabet X, whenever the maximum of lengths of words in W is \(k\ge 3\) and W does not contain the kth power of a letter. This partially answers a problem raised by Jackson et al. (J Algebr 611: 211–245, 2022).

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