Citation: Jongwook Baeck. Correction: On S-principal right ideal rings[J]. AIMS Mathematics, 2023, 8(6): 12694-12695. doi: 10.3934/math.2023638
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On S-principal right ideal rings
by Jongwook Baeck. AIMS Mathematics, 2022, 7(7): 12106–12122.
DOI: 10.3934/math.2022673
The author would like to make the following correction to the published paper [1].
Let R be an associative (not necessarily commutative) ring with unity. If an element e∈R is idempotent, then e(1−e)=0=(1−e)e. Therefore, if e is not a zero-divisor in R, then e must be the unity element. Thus, we should replace "e is not a zero-divisor" with "the multiplicative subsets eS and (1−e)S do not contain the zero element" in [1,Corollary 2.13].
Additionally, to provide an accurate information for the readers, we confirm that the nineteenth paper in [1,References] is published [2].
The change has no material impact on the conclusion of the article. The original manuscript will be updated [1]. We apologize for any inconvenience caused to the readers by this change.
The author declares no conflict of interest.
[1] | J. Baeck, On S-principal right ideal rings, AIMS Math., 7 (2022), 12106–12122. http://doi.org/10.3934/math.2022673 doi: 10.3934/math.2022673 |
[2] | G. Lee, J. Baeck, J. W. Lim, Eakin-Nagata-Eisenbud theorem for right S-Noetherian rings, Taiwanese J. Math., 27 (2023), 237–257. http://doi.org/10.11650/tjm/221101 doi: 10.11650/tjm/221101 |