ON THE m-POTENT RANKS OF CERTAIN SEMIGROUPS OF ORIENTATION PRESERVING TRANSFORMATIONS

Title & Authors
ON THE m-POTENT RANKS OF CERTAIN SEMIGROUPS OF ORIENTATION PRESERVING TRANSFORMATIONS
Zhao, Ping; You, Taijie; Hu, Huabi;

Abstract
It is known that the ranks of the semigroups $\small{\mathcal{SOP}_n}$, $\small{\mathcal{SPOP}_n}$ and $\small{\mathcal{SSPOP}_n}$ (the semigroups of orientation preserving singular self-maps, partial and strictly partial transformations on $X_n Keywords transformation;orientation-preserving;rank;idempotent rank;m-potent rank; Language English Cited by 1. On the (m, r)-potent ranks of certain semigroups of transformations, Journal of Algebra and Its Applications, 2016, 15, 01, 1650018 References 1. G. Ayik, H. Ayik, Y. Unlu, and J. M. Howie, The structure of elements in finite full transformation semigroups, Bull. Aust. Math. Soc. 71 (2005), no. 1, 69-74. 2. P. M. Catarino and P. M. Higgins, The monoid of orientation-preserving mappings on a chain, Semigroup Forum 58 (1999), no. 2, 190-206. 3. V. H. Fernandes, G. M. S. Gomes, and M. M. Jesus, Congruences on monoids of transformations preserving the orientation on a finite chain, J. Algebra 321 (2009), no. 3, 743-757. 4. G. M. S. Gomes and J. M. Howie, On the ranks of certain semigroups of order-preserving transformations, Semigroup Forum 45 (1992), no. 3, 272-282. 5. J. M. Howie, Fundamentals of Semigroup Theory, Oxford, Oxford University Press, 1995. 6. O. Sonmez, Combinatorics of elements in$T_n\;and\;PT_n\$, Int. J. Algebra 4 (2010), no. 1-4, 45-51.

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