On Properties of Generalized Bi-Γ-Ideals of Γ-Semirings

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Bi-Γ-Ideals of Γ-Semirings</title> <meta name="description" content="On Properties of Generalized Bi-Γ-Ideals of Γ-Semirings"> <meta name="keywords" content="Γ-semiring, bi-Γ-ideal, generalized bi-Γ-ideal."> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <meta name="citation_title" content="On Properties of Generalized Bi-Γ-Ideals of Γ-Semirings"> <meta name="citation_author" content="Teerayut Chomchuen"> <meta name="citation_author" content="Aiyared Iampan"> <meta name="citation_publication_date" content="2013/10/05"> <meta name="citation_journal_title" content="International Journal of Mathematical and Computational Sciences"> <meta name="citation_volume" content="7"> <meta name="citation_issue" content="5"> <meta name="citation_firstpage" content="882"> <meta name="citation_lastpage" content="885"> <meta name="citation_pdf_url" content="https://publications.waset.org/17224/pdf"> <link 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introduced by Murali Krishna Rao as a generalization of the notion of Γ-rings as well as of semirings. We have known that the notion of Γ-semirings is a generalization of the notion of semirings. In this paper, extending Kaushik, Moin and Khan’s work, we generalize the notion of generalized bi-Γ-ideals of Γ-semirings and investigate some related properties of generalized bi-Γ-ideals.</p> <iframe src="https://publications.waset.org/17224.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=%CE%93-semiring" title="Γ-semiring">Γ-semiring</a>, <a href="https://publications.waset.org/search?q=bi-%CE%93-ideal" title=" bi-Γ-ideal"> bi-Γ-ideal</a>, <a href="https://publications.waset.org/search?q=generalized%20bi-%CE%93-ideal." title=" generalized bi-Γ-ideal."> generalized bi-Γ-ideal.</a> </p> <p class="card-text"><strong>Digital Object Identifier (DOI):</strong> <a href="https://doi.org/10.5281/zenodo.1335820" target="_blank">doi.org/10.5281/zenodo.1335820</a> </p> <a href="https://publications.waset.org/17224/on-properties-of-generalized-bi-g-ideals-of-g-semirings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/17224/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/17224/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/17224/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/17224/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/17224/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/17224/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/17224/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/17224/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/17224/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/17224/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/17224.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">2293</span> </span> <p class="card-text"><strong>References:</strong></p> <p><br>[1] R. Chinram, A note on quasi-ideals in Γ-semirings, International Mathematical Forum 26 (2008), 1253–1259. <br>[2] ¨O. Bektas¸, N. Bayrak, and A. Ersoy, Soft Γ-semirings, arXiv:1202.1496 (math.RA), 7 Feb 2012. <br>[3] T. K. Dutta and S. K. Sardar, Semiprime ideals and irreducible ideals of Γ-semirings, Novi Sad Journal of Mathematics 30 (2000), 97–108. <br>[4] T. K. Dutta, S. K. Sardar, and S. Goswami, Operations on fuzzy ideals of Γ-semirings, arXiv:1101.4791 (math.RA), 25 Jan 2011. <br>[5] J. Ghosh and T. K. Samanta, Fuzzy ideals in Γ-semiring, arXiv:1010.2469 (math.GM), 12 Oct 2010. <br>[6] R. D. Jagatap and Y. S. Pawar, Quasi-ideals and minimal quasi-ideals in Γ-semirings, Novi Sad Journal of Mathematics 39 (2009), 79–87. <br>[7] J. P. Kaushik, M. A. Ansari, and M. R. Khan, On bi-Γ-ideal in Γ-semirings, International Journal of Contemporary Mathematical Sciences 3 (2008), 1255–1260. <br>[8] S. Lajos, Notes on generalized bi-ideals in semigroups, Soochow Journal of Mathematics 10 (1984), 55–59. <br>[9] S. Pianskool, S. Sangwirotjanapat, and S. Tipyota, Valuation Γ-semirings and valuation Γ-ideals, Thai Journal of Mathematics Special Issue (Annual Meeting in Mathematics) (2008), 93–102. <br>[10] M. Murali Krishna Rao, Γ-semiring I, Southeast Asian Bulletin of Mathematics 19 (1995), 49–54. <br>[11] S. K. Sardar and U. Dasgupta, On primitive Γ-semirings, Novi Sad Journal of Mathematics 34 (2004), 1–12. <br>[12] F. A. Sz´asz, Generalized biideals of rings I, Mathematische Nachrichten 47 (1970), 355–360. <br>[13] F. A. Sz´asz, Generalized biideals of rings II, Mathematische Nachrichten 47 (1970), 361–364.</p> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); });*/ jQuery.get({ url: "https://publications.waset.org/xhr/user-menu", cache: false }).then(function(response){ jQuery('#mainNavMenu').append(response); }); }); </script> </body> </html>

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On Properties of Generalized Bi-Γ-Ideals of Γ-Semirings