The Embedding of Category of Type A Monoid into Inverse Semigroup Categories with Their Translational Hulls

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Paschal Udoka Offor
Chinedu Victor Obasi
Emmanuel Chima Nwamuruamu

Abstract

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.

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How to Cite
Offor, P. U., Obasi, C. V., & Nwamuruamu, E. C. (2025). The Embedding of Category of Type A Monoid into Inverse Semigroup Categories with Their Translational Hulls. Faculty of Natural and Applied Sciences Journal of Mathematical and Statistical Computing, 2(2), 91–102. Retrieved from https://fnasjournals.com/index.php/FNAS-JMSC/article/view/788
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