Year 2019, Volume 48 , Issue 6, Pages 1744 - 1760 2019-12-08

Quasi-normality of idempotents on nilpotents

Tai Keun KWAK [1] , Seung İck LEE [2] , Yang LEE [3]


We study the structure of idempotents in non-Abelian rings, concerning a ring property near to the normality of idempotents on the set of nilpotents. We call a ring with such property right idempotent-quasi-normalizing on nilpotents (simply, right IQNN), and study the structure of right IQNN rings in relation with matrix rings, polynomial ring, and factor rings, by which we extend the class of right IQNN rings. It is proved that the class of IQNN rings contains the $2$ by $2$ full matrix rings over fields and the upper triangular matrix rings over reduced rings. It is shown that given any countable field $K$, there exists a semiprime IQNN algebra $R$ over $K$ such that the polynomial ring $R[x]$ over $R$ is IQNN but not NI, and the upper nilradical of $R[x]$ is zero.
right IQNN ring, idempotent, nilpotent, abelian ring, matrix ring, polynomial ring, NI ring, NR ring
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0001-6316-8650
Author: Tai Keun KWAK (Primary Author)
Institution: Daejin University
Country: South Korea


Orcid: 0000-0002-9612-7844
Author: Seung İck LEE
Institution: Pusan National University
Country: South Korea


Orcid: 0000-0002-7572-5191
Author: Yang LEE
Institution: Daejin University
Country: South Korea


Dates

Publication Date : December 8, 2019

Bibtex @research article { hujms479603, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1744 - 1760}, doi = {10.15672/HJMS.2018.634}, title = {Quasi-normality of idempotents on nilpotents}, key = {cite}, author = {KWAK, Tai Keun and LEE, Seung İck and LEE, Yang} }
APA KWAK, T , LEE, S , LEE, Y . (2019). Quasi-normality of idempotents on nilpotents. Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1744-1760 . DOI: 10.15672/HJMS.2018.634
MLA KWAK, T , LEE, S , LEE, Y . "Quasi-normality of idempotents on nilpotents". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1744-1760 <https://dergipark.org.tr/en/pub/hujms/issue/50516/479603>
Chicago KWAK, T , LEE, S , LEE, Y . "Quasi-normality of idempotents on nilpotents". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1744-1760
RIS TY - JOUR T1 - Quasi-normality of idempotents on nilpotents AU - Tai Keun KWAK , Seung İck LEE , Yang LEE Y1 - 2019 PY - 2019 N1 - doi: 10.15672/HJMS.2018.634 DO - 10.15672/HJMS.2018.634 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1744 EP - 1760 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2018.634 UR - https://doi.org/10.15672/HJMS.2018.634 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Quasi-normality of idempotents on nilpotents %A Tai Keun KWAK , Seung İck LEE , Yang LEE %T Quasi-normality of idempotents on nilpotents %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R doi: 10.15672/HJMS.2018.634 %U 10.15672/HJMS.2018.634
ISNAD KWAK, Tai Keun , LEE, Seung İck , LEE, Yang . "Quasi-normality of idempotents on nilpotents". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1744-1760 . https://doi.org/10.15672/HJMS.2018.634
AMA KWAK T , LEE S , LEE Y . Quasi-normality of idempotents on nilpotents. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1744-1760.
Vancouver KWAK T , LEE S , LEE Y . Quasi-normality of idempotents on nilpotents. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1760-1744.