Some Basic Properties of Weakly Classical Primary and Classical Primary Subsemimodules in Semimodules
Keywords:
semimodule, classical primary subsemimodule, weakly classical primary subsemimodule, -subsemimodule, primary ideal.Abstract
In this paper, we study classical primary and weakly classical primary subsemimodules in semimodules over a semirings. Some characterizations of classical primary and weakly classical primary subsemimodules are obtained. Moreover, we investigate relationships classical primary and weakly classical primary subsemimodules in semimodules over a semirings. Finally, we obtain necessary and sufficient conditions of a weakly classical primary to be a classical primary.
Â
References
Atani R. E., “Prime subsemimodules of semimodulesâ€, International Journal of Algebra, vol. 4, no. 26, pp. 1299- 1306, 2010.
Atani S. E., Darani A. Y., “On quasi-primary submodulesâ€, Chiang Mai J. Sci., vol. 33, no. 3, 249-254, 2006.
Baziar M., Behboodi M., “Classical primary submodules and decomposition theory of modulesâ€, J. Algebra Appl., vol. 8, no. 3, pp. 351-362, 2009.
Behboodi M., Jahani-nezhad R., Naderi M. H., “Classical quasi-primary submodulesâ€, Bulletin of the Iranian Mathematical Society, vol. 37, no. 4, pp. 51-71, 2011.
Dubey M. K., Sarohe P., “On 2-absorbing semimodulesâ€, Quasigroups and Related Systems, vol. 21, pp. 175 - 184, 2013.
Ebrahimi Atani R., “Prime subsemimodules of semimodulesâ€, Int. J.of Algebra, vol. 4, no. 26, pp. 1299 - 1306, 2010.
Ebrahimi Atani R., Ebrahimi Atani S., “On subsemimodules of semimodulesâ€, Buletinul Academiei De Stiinte, vol. 2, no. 63, pp. 20 - 30, 2010.
Ebrahimi Atani S., Shajari Kohan M., “A note on finitely generated multiplication semimodules over comutative semiringsâ€, International Journal of Algebra, vol. 4, no. 8, pp. 389-396, 2010.
Fuchs L., “On quasi-primary idealsâ€, Acta Univ. Szeged. Sect. Sci. Math., vol. 11, pp. 174-183, 1947.
Kamal A.A.M., Al-Shaalan K.H., “Commutativity of near-rings with derivationsâ€, Algebra Colloquium, 2014, vol. 21, no. 2, pp. 215-230, 2014.
Saffar Ardabili J., Motmaen S., Yousefian Darani A., “The spectrum of classical prime subsemimodulesâ€, Australian Journal of Basic and Applied Sciences, vol. 5, no. 11, pp. 1824-1830, 2010.
Srinivasa Reddy M., Amarendra Babu V., Srinivasa Rao P. V., “Weakly primary subsemimodules of partial semimodulesâ€, International Journal of Mathematics and Computer Applications Research (IJMCAR), vol. 3, pp. 45-56, 2013.
Shang Y., “A study of derivations in prime near-ringsâ€, Mathematica Balkanica (New Series), 2011, vol. 25, no. 4, pp. 413-418, 2011.
Tavallaee H.A., Zolfaghari M., “Some remarks on weakly prime and weakly semiprime submodulesâ€, Journal of Advanced Research in Pure Math., vol. 4, no. 1, pp. 19 - 30, 2012.
Tavallaee H.A., Zolfaghari M., “On semiprime submodules and related results, †J. Indones. Math. Soc., vol. 19, no. 1, pp. 49-59, 2013.
Yesilot G., Oral, K. H., Tekir, U., “On prime subsemimodules of semimodulesâ€, International Journal of Algebra, vol. 4, no. 1, pp. 53-60, 2010.
Downloads
Published
How to Cite
Issue
Section
License
- 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.