
This article is cited in 2 scientific papers (total in 2 papers)
RESEARCH ARTICLE
Preradicals, closure operators in $R$Mod and connection between them
A. I. Kashu^{} ^{} Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., Chişinău, MD – 2028 MOLDOVA
Abstract:
For a module category $R$Mod the class $\mathbb{PR}$ of preradicals and the class $\mathbb{CO}$ of closure operators are studied. The relations between these classes are realized by three mappings: $\Phi : \mathbb{CO} \to \mathbb{PR}$ and $\Psi_1, \Psi_2 : \mathbb{PR} \to \mathbb{CO}$. The impact of these mappings on the operations in $\mathbb{PR}$ and $\mathbb{CO}$ (meet, join, product, coproduct) is investigated. It is established that in most cases the considered mappings preserve the lattice operations (meet and join), while the other two operations are converted one into another (i.e. the product into the coproduct and vice versa).
Keywords:
ring, module, lattice, preradical, closure operator, product (coproduct) of closure operators.
Full text:
PDF file (316 kB)
References:
PDF file
HTML file
Bibliographic databases:
MSC: 16D90, 16S90, 06B23 Received: 09.07.2014 Revised: 09.07.2014
Language:
Citation:
A. I. Kashu, “Preradicals, closure operators in $R$Mod and connection between them”, Algebra Discrete Math., 18:1 (2014), 86–96
Citation in format AMSBIB
\Bibitem{Kas14}
\by A.~I.~Kashu
\paper Preradicals, closure operators in $R$Mod and connection between them
\jour Algebra Discrete Math.
\yr 2014
\vol 18
\issue 1
\pages 8696
\mathnet{http://mi.mathnet.ru/adm483}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=3280258}
Linking options:
http://mi.mathnet.ru/eng/adm483 http://mi.mathnet.ru/eng/adm/v18/i1/p86
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:

A. I. Kashu, “A survey of results on radicals and torsions in modules”, Algebra Discret. Math., 21:1 (2016), 69–110

A. I. Kashu, “Pretorsions in modules and associated closure operators”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 24–41

Number of views: 
This page:  168  Full text:  59  References:  27 
