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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 2, Pages 782–791
DOI: https://doi.org/10.33048/semi.2021.18.057
(Mi semr1399)
 

Mathematical logic, algebra and number theory

When a (dual-)Baer module is a direct sum of (co-)prime modules

M. R. Vedadi, N. Ghaedan

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran
References:
Abstract: Since 2004, Baer modules have been considered by many authors as a generalization of the Baer rings. A module $M_R$ is called Baer if every intersection of the kernels of endomorphisms on $M_R$ is a direct summand of $M_R$. It is known that commutative Baer rings are reduced. We prove that if a Baer module $M$ is a direct sum of prime modules, then every direct summand of $M$ is retractable. The converse is true whenever the triangulating dimension of $M$ is finite (e.g. if the uniform dimension of $M$ is finite). Dually, if every direct summand of a dual-Baer module $M$ is co-retractable, then it is a direct sum of co-prime modules and the converse is true whenever the sum is finite or $M$ is a max-module. Among other applications, we show that if $R$ is a commutative hereditary Noetherian ring then a finitely generated $R$-module is Baer iff it is projective or semisimple. Also, over a ring Morita equivalent to a perfect duo ring, all dual-Baer modules are semisimple.
Keywords: Baer module, co-prime module, co-retractable, prime module, dual-Baer, retractable module.
Received January 31, 2021, published July 6, 2021
Bibliographic databases:
Document Type: Article
UDC: 512.55
MSC: 16D10, 16D40, 13C05
Language: English
Citation: M. R. Vedadi, N. Ghaedan, “When a (dual-)Baer module is a direct sum of (co-)prime modules”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 782–791
Citation in format AMSBIB
\Bibitem{VedGha21}
\by M.~R.~Vedadi, N.~Ghaedan
\paper When a (dual-)Baer module is a direct sum of (co-)prime modules
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 2
\pages 782--791
\mathnet{http://mi.mathnet.ru/semr1399}
\crossref{https://doi.org/10.33048/semi.2021.18.057}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000674363700001}
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