On Left Primary and Weakly Left Primary Ideals in LA- Rings
Keywords:
LA-ring, left primary ideal, weakly left primary ideal, left (right) ideal .Abstract
In this paper, we study left ideals, left primary and weakly left primary ideals in LA-rings. Some characterizations of left primary and weakly left primary ideals are obtained. Moreover, we investigate relationships left primary and weakly left primary ideals in LA-rings. Finally, we obtain necessary and sufficient conditions of a weakly left primary ideal to be a left primary ideals in LA- rings.
References
Holgate P.,“Groupoids satisfying a simple invertive lawâ€, Math. Stud., vol. 61, pp. 101–106, 1992.
Kazim M.K., Naseeruddin M., “On almost semigroupsâ€, The Alig. Bull. Math., vol. 2, pp. 1-7, 1972.
Khan M., Ahmad N., “Characterizations of left almost semigroups by their idealsâ€, Journal of Advanced Research in Pure Mathematics, vol. 2, no. 3, pp. 61-733, 2010.
Mushtaq Q., “Abelian groups defined by LA-semigroupsâ€, Studia Scient. Math. Hungar, vol. 18, pp. 427–428, 1983.
Mushtaq Q., Iqbal Q., “Decomposition of a locally associative LA-semigroupâ€, Semigroup Forum, vol. 41, pp. 154– 164, 1990.
Mushtaq Q., Iqbal M., “On representation theorem for inverse LA-semigroupsâ€. Proc. Pakistan Acad. Sci., vol. 30, pp. 247–253, 1993.
Mushtaq Q., Khan M., “A note on an Abel-Grassmann's 3-bandâ€, Quasigroups and Related Systems, vol. 15, pp. 295-301, 2007.
Mushtaq Q., Khan M., “Ideals in left almost semigroupâ€, arXiv:0904.1635v1 [math.GR], 2009.
Rehman I., Shah M., Shah T., Razzaque A., “On existence of nonassociative LA-ringâ€, Analele Stiintfice ale Universitatii Ovidius Constanta, vol. 21, no. 3, pp. 223-228, 2013.
Shah M., Ahmad I., Ali G., “Discovery of new classes of AG-groupoidsâ€, Research Journal of Recent Sciences, vol. 1, no. 11, pp. 47-49, 2012.
Shah T., Ali G., Fazal ur Rehman,“Direct sum of ideals in a generalized LA-ringâ€, International Mathematical Forum, vol. 6, no. 22, 1095 -1101, 2011.
Shah T., Fazal ur Rehman, Raees M. “On near left almost ringsâ€, (to appear).
Shah T., Kausar N., Rehman I. “Fuzzy normal subrings over a nonassociative ringâ€, Analele Stiintfice ale Universitatii Ovidius Constanta, vol. 20, no.1, pp. 369–386, 2012.
Shah T., Raees M., Ali G., “On LA-modulesâ€, Int. J. Contemp. Math. Sciences, vol. 6, no. 21, pp. 999-1006, 2011.
Shah T., Rehman I., Chinram R., “On M-systems in ordered AG-groupoidsâ€, Far East J. Math. Sci., vol. 47, no. 1, pp. 13-21, 2010.
Shah T., Rehman T., Razzaque A., “Soft ordered Abel-Grassman's groupoid (AG-groupoid)â€, International Journal of the Physical Sciences, vol. 6, no.25, pp. 6118-6126, 2010.
Shah T., Rehman I., “On LA-rings of finitely nonzero functionsâ€, Int. J. Contemp. Math. Sciences, vol.5, no.5, pp. 209 -222, 2010.
Shah M., Shah T.,“Some basic properties of LA-ringâ€, International Mathematical Forum, vol. 6, no.44, pp. 2195 - 2199. 2011.
Shah T., Yousaf K., “Topological LA-groups and LA-ringsâ€, Quasigroups and Related Systems, vol. 18, pp. 95 -104, 2010.
Yusuf S.M., “On left almost ringâ€, Proc. of 7th International Pure Math.Conference.
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.