| In this thesis, we study the algebraic structure of maximal left singular lan-guages. In1978H.J.Shyr prove every maximal left singular languages only has only has one left singular word, we use the unique singular word to study the proper-ties and structure of the maximal left singular languages. This thesis construct the methods by a left singular word how to acquire the left singular languages. We prove the production of two maximal left singular languages is not a maximal left singular language. The union of two maximal left singular languages is a maximal left singular language if their left singular words are not the same word. If their left singular words are the same word, then they are same. The intersection of two maximal left singular languages is always a non-empty set. At last, we prove the set of all p-primitive word is a left cancellative language, but it is not a left singular language. The set of2powers of p-primitive word is a left singular language, so it is a left cancellative language and is not a prefix code. The set of i(i>3) powers of p-primitive word is a prefix code, so it is a left cancellative language and a left singular language. |
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