Geodesic
Pseudo semi-projective modules and endomorphism rings
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 4, pp. 557-568

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A module $M$ is called pseudo semi-projective if, for all $\alpha,\beta\in \mathrm{End}_R(M)$ with $\mathrm{Im}(\alpha)=\mathrm{Im}(\beta)$, there holds $\alpha\, \mathrm{End}_R(M)=\beta\, \mathrm{End}_R(M)$. In this paper, we study some properties of pseudo semi-projective modules and their endomorphism rings. It is shown that a ring $ R$ is a semilocal ring if and only if each semiprimitive finitely generated right $R$-module is pseudo semi-projective. Moreover, we show that if $M$ is a coretractable pseudo semi-projective module with finite hollow dimension, then $\mathrm{End}_R(M)$ is a semilocal ring and every maximal right ideal of $\mathrm{End}_R(M)$ has the form $\{s \in \mathrm{End}_R(M) | \mathrm{Im}(s) + \mathrm{Ker}(h)\ne M\}$ for some endomorphism $h$ of $M$ with $h(M)$ hollow.
Keywords: hollow module, finite hollow dimension, perfect ring.
Mots-clés : pseudo semi-projective module 
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     title = {Pseudo semi-projective modules and endomorphism rings},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {557--568},
     publisher = {mathdoc},
     volume = {32},
     number = {4},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VUU_2022_32_4_a4/}
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N. T. T. Ha. Pseudo semi-projective modules and endomorphism rings. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 4, pp. 557-568. http://geodesic.mathdoc.fr/item/VUU_2022_32_4_a4/