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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 10 | Year 2020 | Article Id. IJMTT-V66I10P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I10P521

On Ternary Seminear Rings


R. Vijayakumar, A. Dhivya Bharathi
Abstract

The notion of Ternary seminear ring is introduced which is the generalization of seminear ring. The characterization of ternary seminear ring are derived. The concept of ternary subseminear ring, ideals of ternary seminear ring and ternary seminear ring homomorphism are defined and their properties are also obtained.

Keywords
Seminear ring, ternary semiring, Subseminear ring, Ideal, homomorphism
References

[1] Dutta. T.K. and Kar.S., On regular ternary semirings, Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics, World Scientific, New Jersey,(2003):343-355.
[2] Edmond L. Baker, Near-Rings, Thesis, Denton, Texas, (1972):1-37.
[3] Fawad Hussain, Quotient seminear rings, Indian Journal of Science and Technology,(2016):1-7.
[4] Javed AHSAN, Seminear-rings characterized by their s-ideals I, Proc. Japan Acad, 71(A), (1995):101-103.
[5] Lehmer.D.H., A ternary analogue of abelian groups, Amer.J.Math.,59, (1932):329-338.
[6] Perumal.R., Arulprakasam.R and Radhakrishnan.M.,A note on Ideals in seminear rings, National Conference on Mathematical Techniques and its Applications, (2018):1-6.
[7] Vandiver.H.S., Note on a simple type of Algebra in which the can- cellation law of addition does not hold, Bull. Am. Math. Soc. 40, (1934):914-920.
[8] Willy G. Van Hoorn and van Rootselaar B., Fundemental notions in the theory of Seminearrings, Compositio Math.,18,(1967):65-78.

Citation :

R. Vijayakumar, A. Dhivya Bharathi, "On Ternary Seminear Rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 10, pp. 170-177, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I10P521

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