The monoid of injective and extensive partial transformations of a chain with three elements is nonfinitely based

Abstract

We show that the monoid of all injective and extensive partial transformations of a chain with three elements admits no finite basis of its identities. This completes solving of the finite basis problem for the monoids in the basic frame of partial transformation monoids posed by Volkov.

arXiv commentThe main result of this paper have been obtained in [Xun Hu, Yuzhu Chen, Yanfeng Luo, On the finite basis problem for the monoids of partial extensive injective transformations, Semigroup Forum 91(2015), 524-537]