In real-life structures, indeterminacy is always present. Neuosophic sets theory is a wellknown mathematical tool for dealing with indeterminacy. Smarandache proposed the neutrosophic set approach. Neutrosophic sets deal with vague data. In this study, we introduced and investigated several types of 𝜌 −algebra ideals, which we called neutrosophic 𝜌 −subalgebra, complete neutrosophic 𝜌 −subalgebra, neutrosophic 𝜌 −ideal, complete neutrosophic 𝜌 −ideal, neutrosophic 𝜌̅−ideal, and complete neutrosophic 𝜌̅−ideal, respectively. We also proposed some hypotheses to explain some of the relationships between these ideal types