Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

1-(2-) Prime Ideals in Semirings

  • Nandakumar, Pandarinathan (Department of Mathematics, Perunthalaivar Kamarajar Institute of Engineering and Technology, (Government of Puducherry Institution))
  • Received : 2009.04.25
  • Accepted : 2009.09.10
  • Published : 2010.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we introduce the concepts of 1-prime ideals and 2-prime ideals in semirings. We have also introduced $m_1$-system and $m_2$-system in semiring. We have shown that if Q is an ideal in the semiring R and if M is an $m_2$-system of R such that $\overline{Q}{\bigcap}M={\emptyset}$ then there exists as 2-prime ideal P of R such that Q $\subseteq$ P with $P{\bigcap}M={\emptyset}$.

Keywords

References

  1. J. Ahsan, Fully idempotent semirings, Proc. japan Acad., 69, Ser.A(1993), 185-188.
  2. F.E.Alarcon and D. Polkowska, Fully Prime Semirings, Kyungpook Math. J., 40(2000), 239-245.
  3. P. Dheena and P. Nandakumar, On regular semirings, Indian Journal of Mathematics, 45(2)(2003), 135-140.
  4. N. H. McCoy, Theory of Rings, Macmillan, New York, 1964
  5. M.K.Sen and M.R.Adhikari, On maximal k-ideals of semirings, Proc.Amer. Math.Soc., 118(3), July 1993, 699-703.
  6. M.K.Sen and P.Mukhopadhyay, Von Neumannian Regularity in Semirings, Kyungpook Math.J., 35(1995), 249-258.

Cited by

  1. Contribution to study special kinds of hyperideals in ordered semihyperrings 2017, https://doi.org/10.1016/j.jtusci.2016.09.001
  2. On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings vol.52, pp.1, 2012, https://doi.org/10.5666/KMJ.2012.52.1.91