**Authors:** Caşu Alexei
### Abstract

In this work (which is a continuation of \cite{kas1,kas2,kas3})
the relations between the class $\mathbb C \mathbb O$ of the closure
operators of a module category $R$-Mod and the class $\mathbb P \mathbb R$
of preradicals of this category are investigated. The transition from
$\mathbb C \mathbb O$ to $\mathbb P \mathbb R$ and backwards is
defined by three mappings $\,\Phi : \mathbb C \mathbb O \to \mathbb P \mathbb R\,$
and $\,\Psi_1, \Psi_2 : \mathbb C \mathbb O \to \mathbb P \mathbb R$.
The properties of these mappings are studied. Some monotone bijections are obtained between the preradicals of different
types (idempotent, radical, hereditary, cohereditary, etc.) of
$\mathbb P \mathbb R$ and the closure operators of $\mathbb C \mathbb O$
with special properties (weakly hereditary, idempotent, hereditary, maximal,
minimal, cohereditary, etc.).

Institute of Mathematics and Computer Science

Academy of Sciences of Moldova

5 Academiei str. Chișinău, MD−2028

Moldova

E-mail:

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