Volume 19, Issue 4, pp 246--250
Publication Date: June 21, 2019 Submission Date: March 19, 2019 Revision Date: May 30, 2019 Accteptance Date: June 15, 2019
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### Authors

Phoschanun Ratanaburee - Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. Thananya Kaewnoi - Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. Ronnason Chinram - Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. - Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand.

### Abstract

A ternary semigroup is a nonempty set with a ternary operation satisfy the associative law. In this paper, we define straddles on ternary semigroups and investigate some properties of straddles of ternary semigroups.

### Keywords

• ternary semigroups
• commutative elements
• homomorphisms

•  20N10
•  20M10

### References

• [1] M. Y. Abbasi, S. A. Khan, On some generalized ideals in ternary semigroups, Quasigroups Related Systems, 25 (2017), 181--188

• [2] M. A. Ansari, N. Yaqoob, T-rough ideals in ternary semigroups, Int. J. Pure Appl. Math., 86 (2013), 411--424

• [3] P. Bindu, S. Yella, M. Rao Dasari, $T$-systems in ternary semigroups, Ital. J. Pure Appl. Math., 34 (2015), 221--224

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

• [5] V. N. Dixit, S. Dewan, A note on quasi and bi-ideals in ternary semigroups, Internat. J. Math. Math. Sci., 18 (1995), 501--508

• [6] S. P. Franklin, J. W. Lindsay, Straddles on semigroups, Math. Mag., 34 (1960/61), 269--270

• [7] A. Iampan, Some properties of ideal extensions in ternary semigroups, Iran. J. Math. Sci. Inform., 8 (2013), 67--74

• [8] D. H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math., 54 (1932), 329--338

• [9] J. Łoś, On the extending of models $(I)^*$, Fund. Math., 42 (1955), 38--54

• [10] P. Petchkhaew, R. Chinram, Fuzzy, rough and rough fuzzy ideals in ternary semigroups, Int. J. Pure Appl. Math., 56 (2009), 21--36

• [11] A. M. Rezvi, J. Mehmood, On prime fuzzy bi-ideals in ternary semigroups, Mat. Vesnik, 64 (2012), 79--96

• [12] S. Saelee, R. Chinram, A study on rough, fuzzy and rough fuzzy bi-ideals of ternary semigroups, IAENG Int. J. Appl. Math., 41 (2011), 172--176

• [13] M. L. Santiago, S. Sri Bala, Ternary semigroups, Semigroup Forum, 81 (2010), 380--388

• [14] F. M. Sioson, Ideal theory in ternary semigroups, Math. Japon., 10 (1965), 63--84

• [15] S. Suebsung, R. Chinram, Interval valued fuzzy ideal extensions of ternary semigroups, Int. J. Math. Comput. Sci., 13 (2018), 15--27

• [16] B. Thongkam, T. Changphas, On two-sided bases of ternary semigroups, Quasigroups Related Systems, 23 (2015), 319--324

• [17] N. Yaqoob, M. Khan, M. Akram, A. Khan, Interval valued intuitionistic $(\overline{s}, \overline{t})$-fuzzy ideals of ternary semigroups, Indian J. Sci. Technol., 6 (2013), 5418--5428