Geodesic
On natural and conatural sets of left ideals of a~ring
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2007), pp. 25-32

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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. 
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     author = {A. I. Kashu},
     title = {On natural and conatural sets of left ideals of a~ring},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {25--32},
     publisher = {mathdoc},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2007_2_a2/}
}
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A. I. Kashu. On natural and conatural sets of left ideals of a~ring. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2007), pp. 25-32. http://geodesic.mathdoc.fr/item/BASM_2007_2_a2/