Geodesic
When a (dual-)Baer module is a direct sum of (co-)prime modules
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 782-791.

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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: dual-Baer
Mots-clés : Baer module, co-prime module, co-retractable, prime module, retractable module. 
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M. R. Vedadi; N. Ghaedan. When a (dual-)Baer module is a direct sum of (co-)prime modules. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 782-791. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a1/

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