On Quasi-semiprime and Semiprime Γ -Ideals in Ordered Γ-AG-Groupoids
Keywords:
Γ -AG-Groupoid, Ordered Γ-AG-Groupoid, Γ-ideal, semiprime Γ-ideal, quasi-semiprime Γ-ideal.Abstract
The aim of this short note is to introduce the concepts of quasi-semiprimeand semiprime Γ-ideals in ordered Γ-AG-groupoids with left identity. These concepts are related to the concepts of quasi-semiprime and semiprime Γ-ideals, play an important role in studying the structure of ordered Γ-AG-groupoids, so it seems to be interesting to study them.
References
Faisal N., Yaqoob A., Borumand Saeid, “Some results in bipolar-valued fuzzy ordered AG-groupoidsâ€, Discussiones Mathematicae General Algebra and Applications, vol. 32, pp. 55-57, 2012.
Faisal N., Yaqoob K., Hila, “On fuzzy (2; 2)-regular ordered $Gamma$-AG**-groupoidsâ€, U.P.B. Sci. Bull. Series A, vol. 74. no.2, pp. 87-104, 2012.
Kazim M.A., Naseeruddin M., “On almost semigroupsâ€, The Alig. Bull. Math., vol. 2, pp. 1-7, 1972.
Khan M., Anis S., Shum K.P., “Characterizations of regular ordered Abel-Grassmann groupoidsâ€, International Journal of Algebra, vol. 5., no. 11, pp. 499-521, 2011.
Khan M., Faisal, “On fuzzy ordered Abel-Grassmann's groupoidsâ€, J. Math. Res. (3: 27 - 40, doi: 10.5539/jmr.v3n2p27), 2011.
Khan A., Faisal, Khan W., Yaqoob N., “Ordered LA-semigroups in terms of interval valued fuzzy idealsâ€, Journal of Advanced Research in Pure Mathematics, vol. 5, pp. 100-117, 2013.
Khan M., Naveed Ahmad, “Characterizations of left almost semigroups by their idealsâ€, Journal of Advanced Research in Pure Mathematics, vol. 2, no. 3, pp. 61-73, 2010.
Khan M., Amjid V., Faisal, “Characterizations of intra-regular $Gamma$-AG**-groupoids by the properties of their $Gamma$- idealsâ€, http://arxiv.org/abs/1011.2845 (accessed: 4 September 2013).
Mushtaq Q., Yousuf S.M., “On LA-semigroup defined by a commutative inverse semigroupâ€, Math.Bech., vol. 40, pp. 59-62, 1988.
Mushtaq Q., Yousuf S.M., “On LA-semigroupsâ€. The Alig. Bull. Math., vol. 8, pp. 65-70, 1978.
Naseeruddin M., “Some studies in almost semigroups and flocksâ€, Ph.D. thesis: Aligarh Muslim University: Aligarh: India, 1970.
Protic P.V., Stevanovic N., “AG-test and some general properties of Abel-Grassmann's groupoidsâ€, PU. M. A., vol. 4. no. 6, pp. 371-383, 1995.
Sen M.K., Saha N.K., “On $Gamma$-semigroups Iâ€, Bull. Cal. Math. Soc., vol. 78, pp. 180-186, 1986.
Sen M.K.,“On -semigroupsâ€, Proceeding of International Symposium on Algebra and Its Applications, Decker Publication: New York, pp. 301-308, 1981.
Shah T., Inayatur-Rehman, Razzaque A., “Soft ordered Abel-Grassman's groupoid (AG-groupoid)â€, International Journal of the Physical Sciences, vol. 6., no. 25, pp. 6118-6126, 2011.
Shah T., Rehman I., “On $m$-systems in $Gamma$-AG-groupoidsâ€, Proc. Pakistan Acad.Sci., vol. 47., no. 1, pp. 33-39, 2011.
Shah T., Rehman I., “On $Gamma$-ideals and $Gamma$-bi-ideals in $Gamma$-AG-groupoidsâ€. International Journal of Algebra, vol. 4., no. 6, pp. 267 - 276, 2011.
Shah T., Rehman I., “Decomposition of locally associative $Gamma$-AG-groupoidâ€, Novi Sad J. Math., vol. 43. no. 1, pp. 1-8, 2013.
Downloads
Published
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.