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-R of all unital right R-modules over an associative ring R 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].

中文翻译：

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模完全格上的素数、不可约和完全不可约格前自由基 (I)

基于一个概念格子前自由基最近在 [T. Albu 和 M. Iosif，格罗腾迪克范畴和扭转理论应用的格子前根，J.代数 444(2015) 339–366]，我们在本文中提出并研究了在 Mod-R所有单位的权利R- 关联环上的模块R具有身份，在[F. Raggi、J. Ríos Montes、H. Rincón、R. Fernández-Alonso 和 C. Signoret，素数和不可约的前自由基，J.代数应用程序。 4(2005) 451–466]。