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On $sh$-characteristic submodules. (English)

Authors: Ciocalau R.

Abstract

Submodule ${}_{_{_R}}N\subseteq {}_{_{_R}}M$ is sh-characteristic if there exists a superhereditary preradical $r$ such that $r(M)=N$. (Notation $N\subseteq^{sh}M$). The sh-characteristic submodules are described, in particular $N\subseteq^{sh}M$ iff $N=(0:(0:N)_{_{R}})_{_{M}})$. The properties of the relation $N\subseteq^{sh}M$ permit to transform the set $\Bbb L_{sh}(M)=\{N\in \Bbb L({}_{_R}M) \quad | \quad N\subseteq^{sh} M\}$ in a lattice which is complete, modular and upper continuous.

Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, Chişinău, MD-2028 Moldova