PRIME STRONG IDEALS OF S-SEMIGROUP


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Authors

  • PRAKASH PADOOR Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal
  • BABUSHRI SRINIVAS KEDUKODI Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal,
  • SYAM PRASAD KUNCHAM Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal
  • KAVITHA KOPPULA Manipal Institute of Technology, Manipal Academy of Higher Education

Keywords:

S-semigroup, Seminearring, Prime ideal

Abstract

A seminearring is a generalization of the notion nearring in which the elements need not have an additive inverse. A S-semigroup is a generalization of the notion N-group in which the scalars are from seminearring. In this paper, we define various prime strong ideals of a S-semigroup and obtain the relationship among them. We also establish the connections between completely equiprime, equiprime and completely prime strong ideals of a S-semigroup. The obtained results are illustrated with the suitable examples. We also prove that every equiprime strong ideal of a S-semigroup is 3-prime strong ideal. In addition, we show that (P : Q)S is strong ideal of a seminearring S and prove related results.

References

S. Bhavanari and S.P. Kuncham, Near rings, fuzzy ideals, and graph theory, CRC press New York, USA, 2013.

G.L. Booth, N.J. Groenewald and S. Veldsman, A Kurosh-Amitsur prime radical for near-rings, Commun. Algebra. 18 (1990) 3111-3122. https://doi.org/10.1080/00927879008824063

G.L. Booth and N.J. Groenewald, Equiprime left ideals and equiprime N-groups of a near-ring, Beitr Algebra Geom. 8 (1992) 25-38.

N.J. Groenewald, Dierent prime ideals in near-rings, Commun. Algebra. 19 (1991) 2667-2675. https://doi.org/10.1080/00927879108824287

W.M. Holcombe, Primitive near-rings, Ph.D Thesis. University of Leeds, England, 1970.

S. Juglal, Prime near-ring modules and their links with the generalised group nearring, Ph.D Thesis. Nelson Mandela Metropolitan University, South Africa, 2008.

S. Juglal, N.J. Groenewald and K.S.E. Lee, Dierent prime R-ideals, Algebra Colloq. 17 (2010) 887-904. https://doi.org/10.1142/S1005386710000830

S. Juglal and N.J. Groenewald, Strongly prime near-ring modules, Arab J Sci Eng. 36 (2011) 985-995. https://doi.org/10.1007/s13369-011-0092-2

B.S. Kedukodi, S.P. Kuncham and S. Bhavanari, Equiprime, 3-prime and c-prime fuzzy ideals of nearrings, Soft Comput. 13 (2009) 933-944. https://doi.org/10.1007/s00500-008-0369-x

K. Koppula, B.S. Kedukodi and S.P. Kuncham, On prime strong ideals of a seminearring, Mat. Vesnik. 72 (2020) 243-256.

K. Koppula, B.S. Kedukodi and S.P. Kuncham, Congruences in seminearrings and their correspondence with strong ideals, Algebr. Struct. Appl. (In-Press) (2023).

K. Mogae, Equiprime near-rings, Ph.D Thesis, 2009.

G. Pilz, Near-rings: the theory and its applications, Revised edition, Elsevier, 1983.

P. Prakash, K. Koppula, B.S. Kedukodi and S.P. Kuncham, Isomorphism theorems for S-semigroups with respect to strong ideal, Communicated, (2023).

F. Ta³demir and A.O. Atagün, Equiprime N-ideals of Monogenic N-groups, Hacet. J. Math. Stat. 40 (2011) 375-382.

F. Tasdemir, A.O. Atagün and H. Altndi³, Dierent prime N-ideals and IFP Nideals, Indian J. Pure Appl. Math. 44 (2013) 527-542. https://doi.org/10.1007/s13226-013-0028-5

F. Ta³demir, Completely Equiprime Ideals of Near-Ring Modules, Karaelmas Fen veMüh. Derg. 8 (2018) 79-83.

W.G. VanHoorn and B. VanRootselaar, Fundamental notions in the theory of seminearrings, Composit. Math. 18 (1967) 65-78. http://www.numdam.org/item?id=CM_1967__18_1-2_65_0

S. Veldsman, On equiprime near-rings, Commun. Algebra. 20 (1992) 2569-2587. https://doi.org/10.1080/00927879208824479

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Published

2025-03-10

How to Cite

PADOOR, P., KEDUKODI, B. S., KUNCHAM, S. P., & KOPPULA, K. (2025). PRIME STRONG IDEALS OF S-SEMIGROUP. Results in Nonlinear Analysis, 8(1), 151–162. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/518

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