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Algebra and Discrete Mathematics, 2012, Volume 13, Issue 2, Pages 273–288
(Mi adm77)
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This article is cited in 5 scientific papers (total in 5 papers)
RESEARCH ARTICLE
On inverse operations in the lattices of submodules
A. I. Kashu Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., Chişinău,
MD-2028 MOLDOVA
Abstract:
In the lattice ${\boldsymbol{L}}(_RM)$ 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 $\alpha$-product and $\omega$-coproduct) are defined and studied. Some properties of left quotient with respect to $\alpha$-product and right quotient with respect to $\omega$-coproduct are shown, as well as their relations with the lattice operations in ${\boldsymbol{L}}(_RM)$ (sum and intersection of submodules). The particular case ${}_RM= {}_RR$ of the lattice ${\boldsymbol{L}}(_RR)$ of left ideals of the ring $R$ is specified.
Keywords:
ring, module, preradical, lattice, $\alpha$-product of submodules, left (right) quotient.
Received: 22.02.2012 Accepted: 22.02.2012
Citation:
A. I. Kashu, “On inverse operations in the lattices of submodules”, Algebra Discrete Math., 13:2 (2012), 273–288
Linking options:
https://www.mathnet.ru/eng/adm77 https://www.mathnet.ru/eng/adm/v13/i2/p273
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Abstract page: | 336 | Full-text PDF : | 84 | References: | 44 | First page: | 1 |
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