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Cubic Ideals Of Po-Γ-Semigroups

Authors: V. Chinnadurai; K. Bharathivelan;

Cubic Ideals Of Po-Γ-Semigroups

Abstract

{"references": ["1.\tR. Biswas, \u201cFuzzy Subgroups And Anti Fuzzy Subgroups\u201d, Fuzzy sets and systems, vol.35, no.1, pp.121-124, 1990. 2.\tS.Chattopadhyay, \u201cRight Inverse \u0393-Semigroups\u201d, Bull. cal. math. soc., vol.93, pp.435-442, 2001. 3.\tV. Chinnadurai, \u201cFuzzy Ideals In Algebraic Structures\u201d, Lap lambert academic publishing, Germany, ISBN 10:3659415316/ISBN 13:9783659415319, 2013. 4.\tV. Chinnadurai, \u201cCubic Ideals Of \u0393-Semigroups\u201d, International journal of current research and modern education, vol.1, no.2, pp.140-150, 2016. 5.\tB. Davvaz, Jianming zhan, K.P. Shum, \u201cGeneralized fuzzy submodules endowed with interval-valued membership functions\u201d Information sciences, vol.178, no.15, pp.3147-3159, 2008. 6.\tT.K. Dutta and N.C. Adhikari, \u201cOn \u0393-Semigroups With Right And Left Unities\u201d, Soochow journal of mathematics, vol.19, no.4, pp.461-474, 1993. 7.\tT.K. Dutta and N.C. Adhikari, \u201cOn Prime Radicals Of \u0393-Semigroups\u201d, Bull. calcutta. math. soc., vol.86, no.5, pp.437- 444, 1994. 8.\tT.K. Dutta and N.C. Adhikari, \u201cOn Partially Ordered \u0393-Semigroups\u201d, South east asian bull. math., vol.28, no.6, pp.1021-1028, 2004. 9.\tY. B. Jun, S.T. Jung and M.S. Kim, \u201cCubic Subgroups\u201d, Annals of fuzzy mathematics and informatics, vol.2, no.1, pp.9 -15, 2011. 10.\tY.B. Jun, C.S. Kim and K.O. Yang , \u201cCubic Sets\u201d, Annals of fuzzy mathematics and informatics, vol.4, no.1, pp.83-98, 2012. 11.\tY.B. Jun and Asghar Khan, \u201cCubic Ideals In Semigroups\u201d, Honam mathematical journal, vol.35, no.4, pp.607-623, 2013. 12.\tN. Kuroki, \u201cOn Fuzzy Ideals And Fuzzy Bi-Ideals In Semigroups\u201d, Fuzzy sets and systems, vol.5, no.2, pp.203-215, 1981. 13.\tN. Kuroki, \u201cOn Fuzzy Semigroups\u201d, Information Sciences, vol.53, no.3, pp.203-206, 1991. 14.\tN. Kuroki, \u201cFuzzy Generalized Bi-Ideals In Semigroups\u201d, Informa. Sci., vol.66, no.3, pp.235-243, 1992. 15.\tY.I. Kwon and S.K. Lee, \u201cThe Weakily Semiprime Ideals Of PO-\u0393-Semigroups\u201d, Kangweon-Kyungki Math. Jour., vol.5, no.2, pp.135-139, 1997. 16.\tW.J. Lie, \u201cFuzzy Invariant Subgroups And Fuzzy Ideals\u201d, Fuzzy sets and systems, vol.8, no.2, pp.130-139, 1982. 17.\tS.K. Mujemder and S.K. Sardar, \u201cOn Properties Of Fuzzy Ideals In PO-\u0393-Semigroups\u201d, Armenian journal of mathematics, vol.2, no.2, pp.65-72, 2009. 18.\tA. Rosenfeld, \u201cFuzzy Groups\u201d, Journal of mathematical analysis and applications, vol.35, no.2, pp.512-517, 1971. 19.\tS.K. Sardar, P. Pal, S.K. Majumder and R. Mukherjee, \u201cOn Fuzzy Ideals Of PO-\u0393-Semigroups\u201d, Int. electronic jou. of pure and applied math. vol.5, no.2, pp.79-73, 2012. 20.\tM.K. Sen, \u201cOn \u0393-semigroups\u201d, Algebra and its applications, Lecture notes in pure and applied mathematics 91, Decker, Newyork, 301-308, 1984. 21.\tM.K. Sen and N.K. Saha, \u201cOn \u0393-Semigroups-I\u201d, Bull. of calcutta math. soc., vol.78, no.3, pp.180-186, 1986. 22.\tM. Siripitukdlet and A. Iampan, \u201cOn Ordered Ideal Extensions In A PO-\u0393-Semigroups\u201d, South east asian bulletin of mathematics, vol.33, no.3, pp.543-550, 2009. 23.\tX.Y. Xie, \u201cFuzzy Ideal Extensions Of Semigroups\u201d, Soochow journal of mathematics, vol.27, no.2, pp. 125-138, 2001. 24.\tX.Y. Xie, \u201cFuzzy Ideal Extensions Of Ordered Semigroups\u201d, Lobach journal of mathematics, vol.19, pp.29- 40, 2005. 25.\tL. A. Zadeh, \u201cFuzzy Sets\u201d, Information and computation, vol.8, pp.338-353, 1965."]}

In this paper, we introduce the concept of cubic ideals of po-Γ-semigroups, which is generalized concept of fuzzy ideals of po-Γ-semigroups in order to obtain some characterization theorems. Operator po-semigroups of a po-Γ-semigroup have been made to work by obtaining various relationships between cubic ideals of a po-Γ-semigroup and that of its operator semigroups. We also investigated some of its properties with examples.

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Keywords

Semigroup, Γ-Semigroup, po-Γ-Semigroup, Ideal, Bi-Ideal, Interior Ideal, Cubic Ideal, Cubic Bi-Ideal, Cubic Interior Ideal, Left Operator & Right Operator.

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