Finitely Based Words
Finitely Based Words
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DOI：
10.1142/s0218196700000224
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发表时间：
2000-08
期刊：
影响因子：
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通讯作者：
O. Sapir
中科院分区：
文献类型：
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作者：
O. Sapir
设W是有限语言，Wc是W在取子字下的闭包.设S（W）表示一个自由幺半群在由所有不属于W_c的词组成的理想上的里斯商。如果么半群S（W）是基于W的，我们称W为基于W的。虽然这些半群具有简单的结构，但它们在有限基性质方面表现为“一般”。在本文中，我们描述了所有基于双字母表的单词。我们还找到了一组词是基于语义的一些必要和充分条件。
Let W be a finite language and let Wc be the closure of W under taking subwords. Let S(W) denote the Rees quotient of a free monoid over the ideal consisting of all words that are not in Wc. We call W finitely based if the monoid S(W) is finitely based. Although these semigroups have easy structure they behave "generically" with respect to the finite basis property [6]. In this paper, we describe all finitely based words in a two-letter alphabet. We also find some necessary and some sufficient conditions for a set of words to be finitely based.