Geodesic
Radicals of Generalized Prime Ideals in Ternary Semigroups
Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 2, pp. 395-408.

Voir la notice de l'article provenant de la source Library of Science

In this paper, the concepts of f-prime ideals and f-semiprime ideals on a ternary semigroup are considered as a generalization of pseudo prime ideals and pseudo semiprime ideals, respectively. Then such ideals introduced are used to describe left (respectively, right) f-primary ideals on a ternary semigroup.
Keywords: ternary semigroup, pseudo prime ideal, good mapping, f-prime ideal, left f-primary decomposition 
@article{DMGAA_2022_42_2_a10,
     author = {Satvong, Narakon and Changphas, Thawhat and Luangchaisri, Panuwat},
     title = {Radicals of {Generalized} {Prime} {Ideals} in {Ternary} {Semigroups}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {395--408},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a10/}
}
TY  - JOUR
AU  - Satvong, Narakon
AU  - Changphas, Thawhat
AU  - Luangchaisri, Panuwat
TI  - Radicals of Generalized Prime Ideals in Ternary Semigroups
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2022
SP  - 395
EP  - 408
VL  - 42
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a10/
LA  - en
ID  - DMGAA_2022_42_2_a10
ER  - 
%0 Journal Article
%A Satvong, Narakon
%A Changphas, Thawhat
%A Luangchaisri, Panuwat
%T Radicals of Generalized Prime Ideals in Ternary Semigroups
%J Discussiones Mathematicae. General Algebra and Applications
%D 2022
%P 395-408
%V 42
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a10/
%G en
%F DMGAA_2022_42_2_a10
Satvong, Narakon; Changphas, Thawhat; Luangchaisri, Panuwat. Radicals of Generalized Prime Ideals in Ternary Semigroups. Discussiones Mathematicae. General Algebra and Applications, Tome 42 (2022) no. 2, pp. 395-408. http://geodesic.mathdoc.fr/item/DMGAA_2022_42_2_a10/

[1] S. Bashir and M. Shabir, Pure ideals in ternary semigroups, Quasigroups and Related Systems 17 (2009) 149–160.

[2] P. Choosuwan and R. Chinram, A study on quasi-ideals in ternary semigroups, Int. J. Pure and Appl. Math. 77 (2012) 639–647.

[3] V.N. Dixit and S. Dewan, A note on quasi and bi-ideals in ternary semigroups, Int. J. Math. and Math. Sci. 18 (1995) 501–508. https://doi.org/10.1155/S0161171295000640

[4] T.K. Dutta, S. Kar and B.K. Maity, On ideals in regular ternary semigroups, Discuss. Math. Gen. Alg. and Appl. 28 (2008) 147–159. https://doi.org/10.7151/dmgaa.1140

[5] Z. Gu, On f-prime radical in ordered semigroups, Open Mathematics 16 (2018) 574–580. https://doi.org/10.1515/math-2018-0053

[6] E. Hewitt and H.S. Zuckerman, Ternary operations and semigroups, in: 1969 Semigroups (Proc. Sympos., Wayne State Univ., Detroit, Mich. 1968), (Academic Press, New York, 1968) 55–83.

[7] S. Kar and B.K. Maity, Some ideals of ternary semigroups, Analele Ştiinţifice ale Universităţii Al I Cuza din Iaşi - Matematică LVII (2011) 247–258. https://doi.org/10.2478/v10157-011-0024-1

[8] K. Murata, Y. Kurata and H. Marubayashi, A generalization of prime ideals in rings, Osaka J. Math. 6 (1969) 291–301.

[9] E. Kasner, An extension of the group concept, Bull. Amer. Math. Soc. 10 (1904) 290–291.

[10] D.M. Rao and Y. Sarala, A study on d-system, m-system and n-system in ternary semigroups, Int. J. Development Res. 4 (2014) 195–199.

[11] M.L. Santiago and S. Sri Bala, Ternary semigroups, Semigroup Forum 81 (2010) 380–388. https://doi.org/10.1007/s00233-010-9254-x

[12] S.K. Sardar and S. Goswami, f-prime radical of semirings, South. Asian Bull. Math. 35 (2011) 319–328.

[13] M. Shabir and M. Bano, Prime bi-ideals in ternary semigroups, Quasigroups and Related Systems 16 (2008) 239–256.