Abstract:
The natural and conatural sets of left ideals of a ring $R$ are defined by analogy with natural and conatural classes of left $R$-modules [4,5]. Some characterizations and properties of such sets are indicated. The lattices of natural sets $R$-Nat and of conatural sets $R$-Conat of $R$ are treated as skeletons of more wide lattices of closed and coclosed sets. In particular, $R$-Nat and $R$-Conat are boolean lattices.
Keywords and phrases:(co)natural class of modules, (co)natural set of left ideals, boolean lattice.
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