Abstract
Based on the concept of a lattice preradical recently introduced in [T. Albu and M. Iosif, Lattice preradicals with applications to Grothendieck categories and torsion theories, J. Algebra 444 (2015) 339–366], we present and investigate in this paper, the latticial counterparts of the concepts of prime and irreducible preradicals on the category Mod-[Formula: see text] of all unital right [Formula: see text]-modules over an associative ring [Formula: see text] with identity, introduced and studied in [F. Raggi, J. Ríos Montes, H. Rincón, R. Fernández-Alonso and C. Signoret, Prime and irreducible preradicals, J. Algebra Appl. 4 (2005) 451–466].
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