- seminear-ring,
- congruence relation,
- c-ideal,
- quotient seminear-ring,
- quotient seminear-ring endomorphism
Copyright (c) 2022 Meryta Febrilian Fatimah, Fitriana Hasnani, Nikken Prima Puspita
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Abstract
A seminear-ring is a generalization of ring. In ring theory, if is a ring with the multiplicative identity, then the endomorphism module is isomorphic to . Let be a seminear-ring. Here, we can construct the set of endomorphism from to itself denoted by . We show that if is a seminear-ring, then is also a seminear-ring over addition and composition function. We will apply the congruence relation to get the quotient seminear-ring endomorphism. Furthermore, we show the relation between c-ideal and congruence relations. So, we can construct the quotient seminear-ring endomorphism with a c-ideal.
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References
- W. A. Adkins and S. H. Weintraub, Algebra: An Approach via Module Theory, New York: Springer-Verlag, 1992.
- S. Wahyuni, I. E. Wijayanti, D. A. Yuwaningsih and A. D. Hartanto, Teori Ring dan Modul, Yogyakarta: Gadjah Mada University Press, 2016.
- J. B. Fraleigh, A First Course in Abstract Algebra Seventh Edition, London: Pearson, 2003.
- R. E. Atani and S. E. Atani, “Ideal Theory in Commutative Semirings,” Buletinul Academiei De Stiinte A Republich Moldova Matematica, vol. 2, no. 57, pp. 14-23, 2008.
- W. G. v. Hoorn and B. v. Rootselar, “Fundamental Notions in the Theory of Seminear-rings,” Compositio Mathematica, vol. 18, no. 1-2, pp. 65-78, 1967.
- G. Pilz, Near-Rings, Amsterdam: North-Holland Publishing Company, 1983.
- V. V. Ramachandram, “Comutativity of Semi Near Rings,” Journal of Science and Arts, vol. 4, no. 17, pp. 367-368, 2011.
- J. S. Golan, Semirings and Affine Equations over Them: Theory and Applications, Netherland: Kluwer Academic Publishers, 2003.
- J. M. Howie, Fundamentals of Semigroup Theory, New York: Oxford University Press Inc, 1995.
- C. C. Pinter, Set Theory, Boston: Addison-Wesley Publishing Company Inc, 1971.
- F. Hussain, M. Tahir, S. Abdullah and N. Sadiq, “Quotient Seminear-Rings,” Indian Journal of Science and Technology, vol. 9, no. 38, pp. 1-7, 2016.
- R. Perumal, R. Arulprakasam and M. Radhakrishnan , “A Note on Ideals in Seminear-Rings,” in National Conference on Mathematical Techniques and its Applications (NCMTA 18), Kattankulathur-India, 2018.
- N. Kornthorng and A. Iampan, “A Note on Right Full k-Ideals in Seminear-Rings,” Journal of Informatics and Mathematical Sciences, vol. 4, no. 3, pp. 255-261, 2012.
- R. Perumal and P. Chinnaraj, “Medial Left Bipotent Seminear-Rings,” in Springer Proceedings in Mathematics and Statistics 139, India, 2015.
- S. Senthil and R. Perumal, “Minimal Prime Ideals in Seminear-Rings,” in IOP Publishing Journal of Physics: Conference Series, Tamil Nadu-India, 2020.
- F. Hasnani, M. F. Fatimah and N. P. Puspita, “The notions of irreducible ideals of the endomorphism ring on the category of rings and the category of modules,” Al-Jabar : Jurnal Pendidikan Matematika, vol. 13, no. 1, pp. 101 - 107, 2022.