Geodesic
On partial inverse operations in the lattice of submodules
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2012), pp. 59-73.

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In the present work two partial operations in the lattice of submodules $\boldsymbol L(_RM)$ are defined and investigated. They are the inverse operations for $\omega$-product and $\alpha$-coproduct studied in [6]. This is the continuation of the article [7], in which the similar questions for the operations of $\alpha$-product and $\omega$-coproduct are investigated. The partial inverse operation of left quotient $N\,/_\odot\,K$ of $N$ by $K$ with respect to $\omega$-product is introduced and similarly the right quotient $N\,_:\backslash\,K$ of $K$ by $N$ with respect to $\alpha$-coproduct is defined, where $N,K\in\boldsymbol L(_RM)$. The criteria of existence of such quotients are indicated, as well as the different forms of representation, the main properties, the relations with lattice operations in $\boldsymbol L(_RM)$, the conditions of cancellation and other related questions are elucidated. 
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A. I. Kashu. On partial inverse operations in the lattice of submodules. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2012), pp. 59-73. http://geodesic.mathdoc.fr/item/BASM_2012_2_a4/

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