Some Properties of Hybrid Ideals in Rings

The concept of hybrid left (resp., right) ideals in rings is introduced and a few distinct features are looked into. Using these notions, characterizations of rings and hybrid left (resp., right) ideals are discussed. The hybrid product in the ring is also introduced and characterization of hybrid left (resp., right) ideals is considered by using the notions of hybrid product. We demonstrate this by showing a hybrid left (resp., right) ideal \(d_\eta\) of a ring \(R\) is a hybrid maximal ideal if and only if \(d_\eta(0)=1\) and \(d_{\eta_*}=\{u \in R: d_\eta(u)=d_\eta=(0)\}\) is a maximal left (., right) ideals of \(R\).