Abstract
For an element a in a semigroup S, the local subsemigroup of S with respect to a is the subsemigroup aSa of S. Here we study the structure of local subsemigroups of full transformation semigroups and symmetric inverse monoids. We obtain some results regarding the local subsemigroups and when they are isomorphic to the semigroup itself. Further it is also shown that the set of all local subsemigroups of all finite symmetric inverse monoids and the set of all variants of all finite symmetric inverse monoids is same up to isomorphism.
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References
Araújo, J., Bentz, W., Konieczny, J.: Directed graphs of inner translations of semigroups. Semigroup Forum 94, 650–673 (2016). https://doi.org/10.1007/s00233-016-9821-x
Chase, K.: Sandwich semigroups of binary relations. Discrete Math. 28(3), 231–236 (1979)
Clifford, A.H., Preston, G.B.: The algebraic theory of semigroups, vol. I. Mathematical Surveys. American Mathematical Society, Providence, R.I (1961)
Dolinka, I., Durdev, I., East, J., Honyam, P., Sangkhanan, K., Sanwong, J., Sommanee, W.: Sandwich semigroups in locally small categories II: transformations. Algebra Univers. 79 (2018). https://doi.org/10.1007/s00012-018-0539-3
Dolinka, I., East, J.: Variants of finite full transformation semigroups. Int. J. Algebra Comput. 25(8), 1187–1222 (2015). https://doi.org/10.1142/S021819671550037X
East, J.: Transformation representations of sandwich semigroups. Exp. Math. 29(3), 291–295 (2020). https://doi.org/10.1080/10586458.2018.1459963
Ganyushkin, O., Mazorchuk, V.: Classical Finite Transformation Semigroups: An Introduction. Algebra and Applications. Springer, London (2009)
Hickey, J.B.: Semigroups under a sandwich operation. Proc. Edinburgh Math. Soc.(2) 26(3), 371–382 (1983)
Howie, J.M.: Fundamentals of Semigroup Theory. London Mathematical Society Monographs New Series, Vol. 2. The Clarendon Press, Oxford University Press, New York (1995)
Mitchel, J.D. et al.: Semigroups-GAP Package, version 3.0.20 (2018)
The GAP Group, GAP-Groups, Algorithms and Programming, version 4.10.0 (2018)
Tsyaputa, G.Y.: Transformation semigroups with the deformed multiplication. Bullet. Univ. Kiev. Series: Mech. Math. 3(1), 82–88 (2003)
Tsyaputa, G.Y.: Green’s relations on the deformed transformation semigroups. Algebra Discrete Math. 1, 121–131 (2004)
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Michael, S., Romeo, P.G. (2022). Local Subsemigroups and Variants of Some Classes of Semigroups. In: Ashraf, M., Ali, A., De Filippis, V. (eds) Algebra and Related Topics with Applications. ICARTA 2019. Springer Proceedings in Mathematics & Statistics, vol 392. Springer, Singapore. https://doi.org/10.1007/978-981-19-3898-6_16
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DOI: https://doi.org/10.1007/978-981-19-3898-6_16
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