On pseudocomplements and supplements in the big lattice of preradicals

Abstract

In this paper, we consider aspects of the big lattice of preradicals, related to pseudocomplements and supplements. We consider essential preradicals and superfluous preradicals, and we characterize the situation in which all nonzero preradicals are essential as well as the one in which all proper preradicals are superfluous. Also, we give two different proofs of the known fact that the big lattice of preradicals is strongly pseudocomplemented.