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http://dx.doi.org/10.4134/CKMS.c150164

ON WEAKLY COMPLETELY QUASI PRIMARY AND COMPLETELY QUASI PRIMARY IDEALS IN TERNARY SEMIRINGS  

Yiarayong, Pairote (Department of Mathematics Faculty of Science and Technology Pibulsongkram Rajabhat University)
Publication Information
Communications of the Korean Mathematical Society / v.31, no.4, 2016 , pp. 657-665 More about this Journal
Abstract
In this investigation we studied completely quasi primary and weakly completely quasi primary ideals in ternary semirings. Some characterizations of completely quasi primary and weakly completely quasi primary ideals were obtained. Moreover, we investigated relationships between completely quasi primary and weakly completely quasi primary ideals in ternary semirings. Finally, we obtained necessary and sufficient conditions for a weakly completely quasi primary ideal to be a completely quasi primary ideal.
Keywords
ternary semiring; completely quasi primary; weakly completely quasi primary; k-ideal;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 S. Bashir and M. Shabir, Pure ideals in ternary semigroups, Quasigroups Related Systems 17 (2009), no. 2, 149-160.
2 S. K. Bhambri, M. K. Dubeyand, and Anuradha, On prime, weakly prime left ideals and weakly regular ternary semirings, Southeast Asian Bull. Math. 37 (2013), no. 6, 801-811.
3 T. Changphas, m-systems and n-systems in ordered ternary semigroups, Gen. Math. Notes 7 (2011), no. 2, 59-62.
4 T. Changphas, On maximal ideals in ternary semigroups, Int. J. Pure Appl. Math. 92 (2014), no. 1, 133-139.
5 P. Choosuwan and R. Chinram, A study on quasi-ideals in ternary semigroups, Int. J. Pure Appl. Math. 77 (2012), no. 5, 639-647.
6 V. N. Dixit and S. Dewan, A note on quasi and bi-ideals in ternary semigroup, Int. J. Math. Math. Sci. 18 (1995), no. 3, 501-508.   DOI
7 V. N. Dixit and S. Dewan, Minimal quasi-ideals in ternary semigroup, Indian J. Pure Appl. Math. 28 (1997), no. 5, 625-632.
8 T. K. Dutta and S. Kar, On regular ternary semirings: Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics, 343-355, World Scientific, 2003.
9 T. K. Dutta and S. Kar, On prime ideals and prime radical of ternary semirings, Bull. Calcutta Math. Soc. 97 (2005), no. 5, 445-454.
10 T. K. Dutta, S. Kar, and B. K. Maity, On ideals in regular ternary semigroups, Discuss. Math. Gen. Algebra Appl. 28 (2008), no. 2, 147-159.   DOI
11 A. Iampan, Lateral ideals of ternary semigroups, Ukr. Mat. Visn. 4 (2007), no. 4, 525-534.
12 P. Jailoka and A. Iampan, Minimality and maximality of ordered quasi-ideals in ordered ternary semigroups, Gen. Math. Notes 21 (2014), no. 2, 42-58.
13 S. Kar and K. Das, On k-regular ternary semirings, Proceedings of the International Conference on Algebra 2010, 356-368, World Sci. Publ., Hackensack, NJ., 2012.
14 S. Kar and B. K. Maity, Congruences on ternary semigroups, J. Chungcheong Math. Soc. 20 (2007), no. 3, 191-201.
15 N. Kehayopulu, m-systems and n-systems in ordered ternary semigroups, Quasigroups Related Systems 11 (2014), 55-58.
16 D. H. Lehmer, A ternary analogue of Abelian groups, Amer. J. Math. (1932), no. 2, 329-338.
17 J. Los, On the extending of model I, Fund. Math. 42 (1955), 38-54.   DOI
18 D. Madhusduhana Rao and G. Srinivasa Rao, A study on ternary semirings, Int. J. Math. Archive 5 (2014), no. 12, 24-30.
19 M. Shabir and M. Bano, Prime bi-ideals in ternary semigroups, Quasigroups Related Systems 16 (2008), no. 2, 239-256.
20 F. M. Sioson, Ideal theory in ternary semigroups, Math. Japon. 10 (1965), 63-84.
21 N. Yaqoob, S. Abdullah, N. Rehman, and M. Naeem, Roughness and fuzziness in ordered ternary semigroups, World Appl. Sci. J. 17 (2012), no. 12, 1683-1693.