Characterization of Regularity on Elements in the Bicyclic Semigroup

Main Article Content

Nares Sawatraksa
Chanya Lekjaroensri
Panthakan Wetchakorn
Patcharaporn Sitong

Abstract

Article Details

How to Cite
Sawatraksa, N., Lekjaroensri, C., Wetchakorn, P., & Sitong, P. (2024). Characterization of Regularity on Elements in the Bicyclic Semigroup. PKRU SciTech Journal, 8(2), 53–64. Retrieved from https://ph01.tci-thaijo.org/index.php/pkruscitech/article/view/257368
Section
Research Articles

References

Krohn, K., Rhodes, J. L., & Arbib, M. A. (1968). Algebraic theory of machines, languages, and semigroups. New York: Academic Press.

Arbib, M. A. (1969). Theories of abstract automata (Prentice-Hall series in automatic computation). Prentice-Hall, Inc.

Boorman, S. A., & White, H. C. (1976). Social structure from multiple networks. II. Role structures. American journal of sociology, 81(6), 1384–1446.

Boyd, J. P., Haehl, J. H., & Sailer, L. D. (1972). Kinship systems and inverse semigroups. Journal of Mathematical Sociology, 2(1), 37–61.

Reddy, P. S. (2015). Applications of semigroups. Global Journey of Science Frontier Research, 15(F3), 17–25.

Clifford, A. H. (1941). Semigroups admitting relative inverses. Annals of Mathematics, 42(4), 1037–1049.

Croisot, R. (1953). Demi-groupes inversifs et demi-groupes réunions de demi-groupes simples. In Annales scientifiques de l'École normale supérieure, 70(4), 361–379.

Petrich, M., & Reilly, N. R. (1999). Completely regular semigroups. New York: Wiley.

Lyapin, E. (1953). Canonical form of elements of an associative system given by defining relations. Leningradskii Gosudarstvennyii Pedagogicheskii Institut Uchenye Zapiski, 89,

–54.

Hovsepyan, K. H. (2020). Inverse subsemigroups of the bicyclic semigroup. Mathe-matical Notes, 108, 550–556.

Gutik, O., Prokhorenkova, O., & Sekh, D. (2022). On endomorphisms of the bicyclic semigroup and the extended bicyclic semigroup. DOI:10.30970/vmm.2021.92.005-016

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.

Kudryavtsev, D. (2024). Restrictions on local embeddability into finite semigroups. Semigroup Forum, 109, 148–166

Clifford, A. H., & Preston, G. B. (1961). The algebraic theory of semigroups, vol. 1. Providence: American Mathematical Society.