The Embedding of Category of Type A Monoid into Inverse Semigroup Categories with Their Translational Hulls - Offor, Paschal Udoka; Obasi, Chinedu Victor; Nwamuruamu, Emmanuel Chima (Faculty of Natural and Applied Sciences Journal of Mathematical and Statistical Computing, 2025)
According to Fountain (1979), type A semigroup is characterized as follows: that ???? is a type ???? semigroup if and only if there are inverse semigroups ????1,????2, and embeddings ????1:????→????1, ????2:????→????2, such that ????1????∗=(????1????)∗=(????1????)−1(????1????), ????2????†=(????2????)†=(????1????)(????1????)−1. With full transformation semigroup, this characterization leads to faithful representation of type A semigroup. Offor et al. (2018) extended the representation to the translational hull of type A semigroup. In this paper, we are further extending the representation to the category of the translational hull of type A monoid.