1-(2-) Prime Ideals in Semirings

• Journal title : Kyungpook mathematical journal
• Volume 50, Issue 1,  2010, pp.117-122
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2010.50.1.117
Title & Authors
1-(2-) Prime Ideals in Semirings
Nandakumar, Pandarinathan;

Abstract
In this paper, we introduce the concepts of 1-prime ideals and 2-prime ideals in semirings. We have also introduced $\small{m_1}$-system and $\small{m_2}$-system in semiring. We have shown that if Q is an ideal in the semiring R and if M is an $\small{m_2}$-system of R such that $\small{\overline{Q}{\bigcap}M={\emptyset}}$ then there exists as 2-prime ideal P of R such that Q $\small{\subseteq}$ P with $\small{P{\bigcap}M={\emptyset}}$.
Keywords
Semirings;Prime ideal;Semiprime ideal;
Language
English
Cited by
1.
On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings,;

Kyungpook mathematical journal, 2012. vol.52. 1, pp.91-97
1.
Contribution to study special kinds of hyperideals in ordered semihyperrings, Journal of Taibah University for Science, 2016
2.
On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings, Kyungpook mathematical journal, 2012, 52, 1, 91
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