Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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CORRIGENDUM ON "ORIENTED TRANSFORMATIONS ON A FINITE CHAIN: ANOTHER DESCRIPTION" [COMMUN. KOREAN MATH. SOC. 38 (2023), NO. 3, PP. 725-731]

  • Vitor H. Fernandes (Center for Mathematics and Applications (NOVA Math) and Department of Mathematics Faculdade de Ciencias e Tecnologia Universidade Nova de Lisboa)
  • Received : 2024.01.09
  • Accepted : 2024.03.11
  • Published : 2024.07.31
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Abstract

In this note, we aim to correct some of the results presented in [1]. Namely, the statements of Proposition 2.1, Corollary 2.2, Corollary 2.3, Theorem 2.4 and Theorem 2.6, concerning only the monoids 𝓞𝓟n and 𝓟𝓞𝓟n, have to exclude transformations of rank two. All other results of [1], as well as those mentioned above but for the monoids 𝓞𝓡n and 𝓟𝓞𝓡n, do not require correction.

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Acknowledgement

This work is funded by national funds through the FCT - Fundacao para a Ciencia e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020(https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications).

References

  1. V. H. Fernandes, Oriented transformations on a finite chain: another description, Commun. Korean Math. Soc. 38 (2023), no. 3, 725-731. https://doi.org/10.4134/CKMS.c220272
  2. P. M. Higgins and A. Vernitski, Orientation-preserving and orientation-reversing mappings: a new description, Semigroup Forum 104 (2022), no. 2, 509-514. https://doi.org/10.1007/s00233-022-10256-8
  3. I. Levi and J. D. Mitchell, On rank properties of endomorphisms of finite circular orders, Comm. Algebra 34 (2006), no. 4, 1237-1250. https://doi.org/10.1080/00927870500454091