PO- Ternary Г- Radicals In PO- Ternary Г- Semirings
DOI:
https://doi.org/10.29284/8vw67692Keywords:
prime PO Г- radical, completely prime PO Г- radical, Prime, Semiprime, Completely semiprime.Abstract
This paper presents an investigation of Γ-radicals in the setting of PO-ternary Γ-semirings. We define the notion of Γ-radicals appropriate to partially ordered ternary operations and analyze their key algebraic characteristics. The study examines connections between radicals, ideals, and congruence relations, emphasizing the role of the order structure. Several foundational results concerning existence, characterization, and homomorphic behavior are obtained. The work broadens radical theory to ordered ternary semiring systems and establishes directions for further exploration.References
1. P. J. Allen. A fundamental theorem of homomorphism for semirings. Proc. Amer. Math.Soc., 21(2)(1969), 412–416.
2. T. K. Dutta and S. K. Sardar. On the operator semirings of a Γ−semiring. Southeast AsianBull. Math., 26(2)(2002), 203–213.
3. R. A. Good and D. R. Hughes. Associated groups for a semigroup. Bull. Amer. Math. Soc.,58 (1952), 624–625.
4. M. Henriksen. Ideals in semirings with commutative addition. Notices Amer. Math. Soc.,6(1958), 321.
5. K. Iseki. Ideal theory of semiring. Proc. Japan Acad., 32(8((1956), 554–559.
6. K. Iseki. Ideals in semirings. Proc. Japan Acad., 34(1)(1958), 29–31.
7. K. Iseki. Quasi-ideals in semirings without zero. Proc. Japan Acad., 34(2)(1958), 79–84.
8. K. Izuka. On the Jacobson radical of a semiring. Tohoku Math. J., 11(3)(1959), 409–421.
9. R. D. Jagatap and Y. S. Pawar. Quasi-ideals and minimal quasi-ideals in Γ−semirings. NoviSad J. Math., 39(2)(2009), 79–87.
10. R. D. Jagatap and Y. S. Pawar. Bi-ideals in Γ− semirings. Bull. Int. Math. Virtual Inst.,6(2)(2016), 169–179.
11. S. Lajos. On the bi-ideals in semigroups. Proc. Japan Acad., 45(8)(1969), 710–712.
12. S. Lajos and F. A. Szasz. On the bi-ideals in associative ring. Proc. Japan Acad., 46(6)(1970), 505–507.
13. H. Lehmer. A ternary analogue of Abelian groups. Amer. J. Math., 54(2)(1932), 329–
a. 338.
14. W. G. Lister. Ternary rings. Trans. Amer. Math. Soc., 154 (1971), 37–55.
15. N. Nobusawa. On a generalization of the ring theory. Osaka. J. Math., 1(1)(1964), 81–89.
16. M. M. K. Rao. Γ−semirings - I. Southeast Asian Bull. Math., 19(1)(1995), 49–54.
17. M. M. K. Rao. Γ-semirings - II. Southeast Asian Bull. Math., 21(3)(1997), 281–287.
18. M. M. K. Rao. The Jacobson radical of Γ-semiring. Southeast Asian Bull. Math., 23(1)(1999), 127–134
19. M. M. K. Rao and B. Venkateswarlu. Regular Γ−incline and field Γ−semiring. Novi Sad J.Math., 45(2)(2015), 155–171.
20. M. M. K. Rao. Γ− semiring with identity. Disc. Math. Gen. Alg. Appl., 37(2)(2017), 189–207.
21. M. M. K. Rao. Bi-quasi-ideals and fuzzy bi-quasi ideals of Γ−semigroups. Bull. Int. Math.Virtual Inst., 7(2)(2017), 231–242.
22. M. M. K. Rao. Ideals in ordered Γ−semirings. Disc. Math. Gen. Alg. and Appl., 38(1)(2018), 47–68.
23. M. M. K. Rao. Bi-interior Ideals in semigroups. Disc. Math. Gen. Alg. Appl., 38(1)(2018),69–78.
24. M. M. K. Rao. Left bi-quasi ideals of semirings. Bull. Int. Math. Virtual Inst. , 8(1)(2018),45–53.
25. M. M. K. Rao. A study of bi-quasi interior ideal as a new generalization of ideal of generalization of semiring. J. Int. Math. Virtual Inst., 9(1)(2019), 19–35.
26. M. M. K. Rao. Quasi - interior ideals of semirings. Bull. Int. Math. Virtual Inst., 9(1)(2019),231–242.
27. M. M. K. Rao and B. Venkateswarlu. On generalized right derivations of incline. J. Int. Math. Virtual Inst., 6(2016), 31–47.
28. M. M. K. Rao and B. Venkateswarlu. Right derivation of ordered Γ−semirings. Disc. Math. Gen. Alg. Appl.,36 (2016), 209–221.
29. M. M. K. Rao, B. Venkateswarlu and N. Rafi. Left bi-quasi-ideals of Γ−semirings. Asia Paci. J. Math., 4(2)(2017), 144–153.
30. G. Srinivasa Rao P.Siva Prasad, M. Vasantha, Dr. D. Madhusudhana Rao “On Strongly Duo and Duo Left Γ-TS-Acts over ternary-semigroups”, International Journal of Pure and Applied Mathematics Volume 113 No. 6 2017, 65 – 73, ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-
31. line version) PP 67-73.
32. Ch. ManikyaRao P.Siva Prasad, D. Madhusudhana Rao, G. SrinivasaRao,”Maximal ideal of compact connected topological ternary semigroups” International conference on mathematics 2015,At: kerela,Volume: Volume 4 Issue 2.
33. P. Sivaprasad , Dr. D. Madhusudhana Rao , G. Srinivasa Rao,” A STUDY ON STRUCTURE OF PO-TERNARY SEMIRINGS”, JOURNAL OF ADVANCES IN MATHEMATICS, Vol .10, No.8,PP:3717-3724.
34. P. Sivaprasad , Dr. D. Madhusudhana Rao , Mamidipalli. Vasantha, , B. Srinivasa Kumar,” On Γ-TS-Acts Over Ternary Γ-Semigroups” International Journal of Engineering & Technology, 7 (4.10) (2018)PP:812-815.
35. Siva Prasad.P, Revathi.K, 2, Sundarayya.P , Madhusudhana Rao.D , “Compositions of Fuzzy T-Ideals in Ternary -Semi ring”, International Journal of Advanced in Management, Technology and Engineering Sciences Volume 7, Issue 12, 2017 ISSN NO : 2249- 7455,PP:135-145.
36. P. Sivaprasad,C. Sreemannarayana, D. Madhusudhana Rao, T. Nageswara Rao, K. Anuradha,” On Le- Ternary Semi groups-I” International Journal of Recent Technology and Engineering (IJRTE) ISSN: 2277-3878, Volume-7, Issue-ICETESM, March 2019,PP:165-167.
37. P. Sivaprasad,C. Sreemannarayana, D. Madhusudhana Rao, T. Nageswara Rao, Sajani Lavanya. M,” On Le- Ternary Semi groups-II” International Journal of Recent Technology and Engineering (IJRTE) ISSN: 2277-3878, Volume-7, Issue-ICETESM, March 2019,PP:168-170.
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