Publicado

2020-03-02

Ordered Semihypergroup Constructions

Construcciones de Semihipergrupos Ordenados

Palabras clave:

Ordered semihypergroup, hyperideal, completely regular, duo ordered semihypergroup, bi-hyperideal, intra-regular, quasi-hyperideal (en)
Semihipergrupo ordenado, hiperideal, completamente regular, semihipergrupo ordenado duo, bi-hiperideal, intra-regular, cuasi-hiperideal (es)

Descargas

Autores/as

  • L. Kamali Ardekani Ardakan University
  • B. Davvaz Yazd University
The concept of ordered semihypergroups is a generalization of the concept of ordered semigroups. In this paper, we study some aspects of hyperideals, bi-hyperideals and quasi-hyperideals of ordered semihypergroups. We investigate the notions of regular, intra-regular and completely regular ordered semihypergroups and give their characterizations in terms of hyper-ideals, bi-hyperideals and quasi-hyperideals. Also, the notion of duo ordered semihypergroups is introduced and some related results are discussed.
El concepto de semihipergrupos ordenados es una generalización del concepto de semigrupos ordenados. En este trabajo, estudiamos algunos aspectos de hiperideales, bi-hiperideales y cuasi hiperideales de semihipergrupos ordenados. Investigamos las nociones de semihipergrupos ordenados regulares ideales, intra-regulares y completamente regulares y damos sus caracterizaciones en términos de hiperideales, bi-hiperideales y cuasi-hiperideales. Además, se introduce la noción de semihipergrupos ordenados dúo y se discuten algunos resultados relacionados.

Referencias

N. G. Alimov, On ordered semigroups, Izvestiya Akad. Nauk SSSR. Ser. Mat. 14 (1950), 569-576, (Russian).

T. Changphas and B. Davvaz, Bi-hyperideals and quasi-hyperideals in ordered semihypergroups, Submitted.

T. Changphas and B. Davvaz, Properties of hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 33 (2014), 425-432.

A. H. Clifford, Totally ordered commutative semigroups, Bull. Amer. Math. Soc. 64 (1958), 305-316.

B. Davvaz, P. Corsini, and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseudoorders, European J. Combinatorics 44 (2015), 208-217.

R. A. Good and D. R. Hughes, Associated groups for a semigroup, Bull. Amer. Math. Soc. 58 (1952), 624-625.

D. Heidari and B. Davvaz, On ordered hyperstructures, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 73 (2011), no. 2, 85-96.

K. Hila, B. Davvaz, and K. Naka, On quasi-hyperideals in semihypergroups, Comm. Algebra 39 (2011), no. 11, 4183-4194.

K. M. Kapp, On bi-ideals and quasi-ideals in semigroups, Publ. Math. Debrecen 16 (1969), 179-185.

N. Kehayopulu, On weakly prime ideals in ordered semigroups, Math. Japon 35 (1990), no. 6, 1051-1056.

N. Kehayopulu, On completely regular poe-semigroups, Math. Japon 37 (1992), no. 1, 123-130.

N. Kehayopulu, On prime, weakly prime ideals in ordered semigroups, Semigroup Forum 44 (1992), no. 3, 341-346.

N. Kehayopulu, On intra-regular ordered semigroups, Semigroup Forum 46 (1993), 271-278.

N. Kehayopulu, On regular, regular duo ordered semigroups, Pure Math. Appl. 5 (1994), no. 3, 161-176.

N. Kehayopulu, Remark on ordered semigroups, Abstracts AMS 15 (1994), no. 4, *94T-06-74.

N. Kehayopulu, On completely regular ordered semigroups, Sci. Math. 1 (1998), no. 1, 27-32.

N. Kehayopulu, On regular duo po-T-semigroups, Math. Slovaca 61 (2011), no. 6, 871-884.

N. Kehayopulu and M. Tsingelis, On ordered semigroups which are semi-lattices of left simple semigroups, Math. Slovaca 63 (2013), no. 3, 411-416.

N. Kehayopulu and M. Tsingelis, On ordered semigroups which are semilattices of simple and regular semigroupss, Comm. Algebra 41 (2013), no. 9, 3252-3260.

Y. Kemprasit, Some transformation semigroups whose sets of bi-ideals and quasi-ideals coincide, Comm. Algebra 30 (2002), no. 9, 4499-4506.

S. K. Lee and Y. I. Kwon, On completely regular and quasi-completely regular ordered semigroups, Math. Japon 47 (1998), no. 2, 247-251.

F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934), 45-49.

T. Saito, Ordered idempotent semigroups, J. Math. Soc. Japan. 14 (1962), 150-169.

T. Saito, Regular elements in an ordered semigroup, Pacific J. Math. 13 (1963), 263-295.

R. Saritha, Prime and semiprime bi-ideals in ordered semigroups, Int. J. Algebra 7 (2013), no. 17, 839-845.

M. Shabir, A. Ali, and S. Batool, A note on quasi-ideals in semirings, Southeast Asian Bull. Math. 27 (2004), no. 5, 923-928.

O. Steinfeld, Quasi-ideals in rings and semigroups, With a foreword by L. Rédei. Disquisitiones Mathematicae Hungaricae [Hungarian Mathematics

Investigations], 10. Akadémiai Kiadó, Budapest, 1978.

M. Tsingelis, Contribution to the structure theory of ordered semigroups, Doctoral Dissertation, University of Athens, 1991.

Cómo citar

APA

Ardekani, L. K. y Davvaz, B. (2018). Ordered Semihypergroup Constructions. Boletín de Matemáticas, 25(2), 77–99. https://revistas.unal.edu.co/index.php/bolma/article/view/85489

ACM

[1]
Ardekani, L.K. y Davvaz, B. 2018. Ordered Semihypergroup Constructions. Boletín de Matemáticas. 25, 2 (jul. 2018), 77–99.

ACS

(1)
Ardekani, L. K.; Davvaz, B. Ordered Semihypergroup Constructions. Bol. Matemáticas 2018, 25, 77-99.

ABNT

ARDEKANI, L. K.; DAVVAZ, B. Ordered Semihypergroup Constructions. Boletín de Matemáticas, [S. l.], v. 25, n. 2, p. 77–99, 2018. Disponível em: https://revistas.unal.edu.co/index.php/bolma/article/view/85489. Acesso em: 21 abr. 2025.

Chicago

Ardekani, L. Kamali, y B. Davvaz. 2018. «Ordered Semihypergroup Constructions». Boletín De Matemáticas 25 (2):77-99. https://revistas.unal.edu.co/index.php/bolma/article/view/85489.

Harvard

Ardekani, L. K. y Davvaz, B. (2018) «Ordered Semihypergroup Constructions», Boletín de Matemáticas, 25(2), pp. 77–99. Disponible en: https://revistas.unal.edu.co/index.php/bolma/article/view/85489 (Accedido: 21 abril 2025).

IEEE

[1]
L. K. Ardekani y B. Davvaz, «Ordered Semihypergroup Constructions», Bol. Matemáticas, vol. 25, n.º 2, pp. 77–99, jul. 2018.

MLA

Ardekani, L. K., y B. Davvaz. «Ordered Semihypergroup Constructions». Boletín de Matemáticas, vol. 25, n.º 2, julio de 2018, pp. 77-99, https://revistas.unal.edu.co/index.php/bolma/article/view/85489.

Turabian

Ardekani, L. Kamali, y B. Davvaz. «Ordered Semihypergroup Constructions». Boletín de Matemáticas 25, no. 2 (julio 1, 2018): 77–99. Accedido abril 21, 2025. https://revistas.unal.edu.co/index.php/bolma/article/view/85489.

Vancouver

1.
Ardekani LK, Davvaz B. Ordered Semihypergroup Constructions. Bol. Matemáticas [Internet]. 1 de julio de 2018 [citado 21 de abril de 2025];25(2):77-99. Disponible en: https://revistas.unal.edu.co/index.php/bolma/article/view/85489

Descargar cita

Visitas a la página del resumen del artículo

133

Descargas