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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
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
Аннотация:
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.
Ключевые слова:
ring, module, preradical, lattice, $\alpha$-product of submodules, left (right) quotient.
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Тип публикации:
Статья
MSC: 16D90, 16S90, 06B23
Поступила в редакцию: 22.02.2012
Принята в печать:22.02.2012
Язык публикации: английский
Образец цитирования:
A. I. Kashu, “On inverse operations in the lattices of submodules”, Algebra Discrete Math., 13:2 (2012), 273–288
Цитирование в формате AMSBIB
\RBibitem{Kas12}
\by A.~I.~Kashu
\paper On inverse operations in the lattices of submodules
\jour Algebra Discrete Math.
\yr 2012
\vol 13
\issue 2
\pages 273--288
\mathnet{http://mi.mathnet.ru/adm77}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3027510}
\zmath{https://zbmath.org/?q=an:1258.16012}
Образцы ссылок на эту страницу:
http://mi.mathnet.ru/adm77 http://mi.mathnet.ru/rus/adm/v13/i2/p273
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
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A. I. Kashu, “On partial inverse operations in the lattice of submodules”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 2, 59–73
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A. I. Kashu, “A survey of results on radicals and torsions in modules”, Algebra Discrete Math., 21:1 (2016), 69–110
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Ion Jardan, “On the inverse operations in the class of preradicals of a module category, I”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 1, 57–66
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Ion Jardan, “On the inverse operations in the class of preradicals of a module category, II”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 77–87
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Jardan I., “on Partial Inverse Operations in the Class of Preradicals of Modules”, Analele Stiint. Univ. Ovidius C., 27:2 (2019), 15–36
  
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