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Abstract
In this paper, we discuss the properties of ℒ L ′ = {L′ ∈ M|LL′ ∈ S l }, where M is the monoid of languages and S l is the set of left singular languages in M. The following result is proved: when|A| ≥ 2, for any L ∈ M, ℒ L ′ is not free.
Acknowledgements
The research of the author is supported by a NSF(China) grant # 10071068 and a Yunnan University Youth Foundation # 2002Q017SL. The author thanks her supervisor, Professor Y. Q. Guo, for his guidance and help.