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 L(RM) are defined and investigated. They are the inverse operations for ω-product and α-coproduct studied in [6]. This is the continuation of the article [7], in which the similar questions for the operations of α-product and ω-coproduct are investigated. The partial inverse operation of left quotient N/⊙K of N by K with respect to ω-product is introduced and similarly the right quotient N:∖K of K by N with respect to α-coproduct is defined, where N,K∈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 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. https://geodesic-test.mathdoc.fr/item/BASM_2012_2_a4/

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