The generalized version of Jun's cubic sets in semigroups

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.