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The bicyclic semigroup as the quotient inverse semigroup by any gauge inverse submonoid

Year 2022, , 53 - 61, 13.05.2022
https://doi.org/10.13069/jacodesmath.1112177

Abstract

Every gauge inverse submonoid (including Jones-Lawson's gauge inverse submonoid of the polycyclic monoid $P_{n}$) is a normal submonoid. In 2018, Alyamani and Gilbert introduced an equivalence relation on an inverse semigroup associated to a normal inverse subsemigroup. The corresponding quotient set leads to an ordered groupoid. In this note we shall show that this ordered groupoid is inductive if the normal inverse subsemigroup is a gauge inverse submonoid and the corresponding quotient inverse semigroup by any guage inverse submonoid is isomorphic either to the bicyclic semigroup or to the bicyclic semigroup with adjoined zero.

References

  • [1] N. Alyamani, N. D. Gilbert, Ordered groupoid quotients and congruences on inverse semigroups, Semigroup Forum 96 (2018) 506–522.
  • [2] D. G. Jones, M. V. Lawson, Strong representations of the polycyclic inverse monoids: Cycles and atoms, Period. Math. Hung. 64 (2012) 54–87.
  • [3] M. V. Lawson, Inverse semigroups: the theory of partial symmetries, World Scientific, Singapore (1998).
  • [4] E. D. Schwab, Möbius monoids and their connection to inverse monoids, Semigroup Forum 90 (2015) 694–720.
  • [5] E. D. Schwab, Gauge inverse monoids, Algebra Colloq. 27(2) (2020) 181–192.
Year 2022, , 53 - 61, 13.05.2022
https://doi.org/10.13069/jacodesmath.1112177

Abstract

References

  • [1] N. Alyamani, N. D. Gilbert, Ordered groupoid quotients and congruences on inverse semigroups, Semigroup Forum 96 (2018) 506–522.
  • [2] D. G. Jones, M. V. Lawson, Strong representations of the polycyclic inverse monoids: Cycles and atoms, Period. Math. Hung. 64 (2012) 54–87.
  • [3] M. V. Lawson, Inverse semigroups: the theory of partial symmetries, World Scientific, Singapore (1998).
  • [4] E. D. Schwab, Möbius monoids and their connection to inverse monoids, Semigroup Forum 90 (2015) 694–720.
  • [5] E. D. Schwab, Gauge inverse monoids, Algebra Colloq. 27(2) (2020) 181–192.
There are 5 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Emil Daniel Schwab This is me

Publication Date May 13, 2022
Published in Issue Year 2022

Cite

APA Schwab, E. D. (2022). The bicyclic semigroup as the quotient inverse semigroup by any gauge inverse submonoid. Journal of Algebra Combinatorics Discrete Structures and Applications, 9(2), 53-61. https://doi.org/10.13069/jacodesmath.1112177
AMA Schwab ED. The bicyclic semigroup as the quotient inverse semigroup by any gauge inverse submonoid. Journal of Algebra Combinatorics Discrete Structures and Applications. May 2022;9(2):53-61. doi:10.13069/jacodesmath.1112177
Chicago Schwab, Emil Daniel. “The Bicyclic Semigroup As the Quotient Inverse Semigroup by Any Gauge Inverse Submonoid”. Journal of Algebra Combinatorics Discrete Structures and Applications 9, no. 2 (May 2022): 53-61. https://doi.org/10.13069/jacodesmath.1112177.
EndNote Schwab ED (May 1, 2022) The bicyclic semigroup as the quotient inverse semigroup by any gauge inverse submonoid. Journal of Algebra Combinatorics Discrete Structures and Applications 9 2 53–61.
IEEE E. D. Schwab, “The bicyclic semigroup as the quotient inverse semigroup by any gauge inverse submonoid”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 9, no. 2, pp. 53–61, 2022, doi: 10.13069/jacodesmath.1112177.
ISNAD Schwab, Emil Daniel. “The Bicyclic Semigroup As the Quotient Inverse Semigroup by Any Gauge Inverse Submonoid”. Journal of Algebra Combinatorics Discrete Structures and Applications 9/2 (May 2022), 53-61. https://doi.org/10.13069/jacodesmath.1112177.
JAMA Schwab ED. The bicyclic semigroup as the quotient inverse semigroup by any gauge inverse submonoid. Journal of Algebra Combinatorics Discrete Structures and Applications. 2022;9:53–61.
MLA Schwab, Emil Daniel. “The Bicyclic Semigroup As the Quotient Inverse Semigroup by Any Gauge Inverse Submonoid”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 9, no. 2, 2022, pp. 53-61, doi:10.13069/jacodesmath.1112177.
Vancouver Schwab ED. The bicyclic semigroup as the quotient inverse semigroup by any gauge inverse submonoid. Journal of Algebra Combinatorics Discrete Structures and Applications. 2022;9(2):53-61.