On Prime and Left Prime Ideals in Semirings
Keywords:semiring, ideal, quasi-ideal, left prime, prime.
The purpose of this paper is to introduce the notion of a left prime ideals in semirings, we study prime and left prime ideals in semirings. Some characterizations of prime and left prime ideals are obtained. Moreover, we investigate relationships between prime and left prime ideals in semirings.
Allen P.J., â€œA fundamental theorem of homomorphisms for semiringsâ€, Proc. Amer.Math. Soc., vol. 21, pp. 412- 416, 1969.
Allen P.J., Neggers J., â€œIdeal theory in commutative semiringsâ€, Kyungpook Math.J., vol. 46, pp. 261-271, 2006.
Anderson D.D., Smith E., â€œWeakly prime idealsâ€, Houston Journal of Mathematics, vol. 23, no. 4, pp. 831-840, 2003.
Atani S.E., â€œOn -weakly primary ideals over semirings, sarajevo journal of mathematics, vol. 3, no. 15, pp. 9- 13, 2007.
Atani S.E. â€œThe ideal theory in quotients of commutative semiringsâ€, Glasnik matematicki, vol. 42, no. 62, pp. 301-308, 2007.
Atani S.E., â€œ On primal and weakly primal ideals over commutative semiringsâ€, Glasnik matematicki, vol. 43, no. 63, pp. 13â€“23, 2008.
Atani S.E., Garfami G., â€œIdeals in quotient semiringsâ€. Chiang Mai J. Sci., vol. 40, no. 1, pp. 77-82, 2013.
Chaudhari J.N., Bonde D.R., â€œWeakly prime subsemimodules of semimodules over Semiringsâ€, International Journal of Algebra, vol. 5, no. 4, pp. 167-174, 2011.
Donges C., â€œOn quasi-ideals of semiringsâ€, Clausthal-Zellerfeld, vol. 17, no. 1, pp. 47-58, 1994.
Dubey M.K., â€œPrime and weakly prime ideals in semiringsâ€, Quasigroups and Related Systems, vol. 20, pp. 197- 202, 2012.
Dutta T.K., Das M.L., â€œOn Strongly prime semiringâ€, Bull. Malays. Math. Sci. Soc., vol. 30, no. 2, pp. 135-141, 2007.
Gupta V., Chaudhari J.N., â€œSome remarks on semiringsâ€, Radovi Matematicki, vol. 12, pp. 13-18, 2003.
Henriksen M., Ideals in semirings with commutative additionâ€, Amer. Math. Soc. Noticcs, vol. 6, 321, 1958.
Jana K., â€œQuasi k-ideals in k-regular and intra k-regular semiringsâ€, PU. M. A., vol. 22, no. 1, pp. 65-74, 2011.
Mosher J.R., â€œGeneralized quotients of hemiringsâ€, Compositio Math., vol. 22, pp. 275-281, 1970.
Sen M.K., Mukhopadhyay P., Ghosh S., â€œp-ideals in p-regular semiringsâ€, Southeast Asian Bull. Math., vol. 26, pp. 439-452, 2002.
How to Cite
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.