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 SM ISO690:2012KASHU, A.. On inverse operations in the lattices of submodules. In: Algebra and Discrete Mathematics, 2012, vol. 13, pp. 273-288. ISSN 1726-3255. |
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  Algebra and Discrete Mathematics |
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| Volumul 13 / 2012 / ISSN 1726-3255 | ||||||
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| Pag. 273-288 | ||||||
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In the lattice L( RM) of submodules of an arbitrary left R-module RM four operation were introduced and investigated in the paper [3]. In the present work the approximations of inverse operations for two of these operations (for α-product and ω-coproduct) are defined and studied. Some properties of left quotient with respect to α-product and right quotient with respect to ω-coproduct are shown, as well as their relations with the lattice operations in L( RM) (sum and intersection of submodules). The particular case RM = RR of the lattice L( RR) of left ideals of the ring R is specified. |
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| Cuvinte-cheie α-product of submodules, lattice, Left (right) quotient, module, Preradical, Ring |
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