Affiliations: Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan | Department of Mathematics Education, Gyeongsang National University, Jinju, Korea | Department of Mathematics, Hazara University, Mansehra, Pakistan | Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia | Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
Note: [] Corresponding author. Madad Khan, Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan. E-mails: madadmath@yahoo.com (M. Khan); skywine@gmail.com (Y.B. Jun); gulistanmmath@hu.edu.pk (M. Gulistan); nayaqoob@ymail.com (N. Yaqoob).
Abstract: In this paper, we define the concept of generalized cubic subsemigroups (ideals) of a semigroup and investigate some of its related properties. In particular, we introduce the concept of $(\in _{(\widetilde{\gamma }_{1},\gamma _{2}) },\in _{(\widetilde{\gamma}_{1},\gamma _{2}) }\vee q_{(\widetilde{\delta }_{1},\delta _{2})})$-cubic ideal, $(\in _{( \widetilde{\gamma }_{1},\gamma _{2}) },\in _{(\widetilde{\gamma }_{1},\gamma _{2}) }\vee q_{(\widetilde{\delta }_{1},\delta _{2}) })$-cubic quasi-ideal, $(\in _{( \widetilde{\gamma }_{1},\gamma _{2}) },\in _{(\widetilde{\gamma }_{1},\gamma _{2}) }\vee q_{( \widetilde{\delta }_{1},\delta _{2})})$-cubic bi-ideal and $(\in _{( \widetilde{\gamma }_{1},\gamma _{2})},\in _{(\widetilde{\gamma } _{1},\gamma _{2})}\vee q_{(\widetilde{\delta }_{1},\delta _{2})})$-cubic prime/semiprime ideal of a semigroup.
Keywords: Semigroups, cubic sets, generalized cubic ideals (bi-ideals, interior ideals, quasi ideals, prime ideals)
