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Section
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Mathematics
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Title
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Pseudo semi-projective modules and endomorphism rings
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Author(-s)
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Ha N.T.T.a
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Affiliations
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Industrial University of Ho Chi Minh citya
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Abstract
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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.
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Keywords
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pseudo semi-projective module, hollow module, finite hollow dimension, perfect ring
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UDC
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512.553
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MSC
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16D80, 16D40, 16D90
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DOI
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10.35634/vm220405
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Received
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9 May 2022
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Language
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English
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Citation
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Ha N.T.T. Pseudo semi-projective modules and endomorphism rings, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, vol. 32, issue 4, pp. 557-568.
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