Research Article
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Year 2024, Early Access, 1 - 15
https://doi.org/10.15672/hujms.1413424

Abstract

References

  • [1] H. Chen, Exchange rings with artinian primitive factors, Algebra Represent. Theory. 2, 201–207, 1999.

On products of idempotents and nilpotents

Year 2024, Early Access, 1 - 15
https://doi.org/10.15672/hujms.1413424

Abstract

This article studies the ring structure arising from products of idempotents and nilpotents. Thus the argument is concerned essentially with the one-sided IQNN property of rings. We first prove that if the $2$ by $2$ full matrix ring over a principal ideal domain $F$ of characteristic zero is right IQNN then $F$ contains infinitely many non-integer rational numbers; and that the concepts of right IQNN and right quasi-Abelian are independent of each other. We next introduce a ring property, called {\it right IAN}, as a generalization of both right IQNN and right quasi-Abelian; and provide several kinds of methods to construct right IAN rings. In the procedure, we also show that the right IQNN and right IAN do not go up to polynomial rings.

References

  • [1] H. Chen, Exchange rings with artinian primitive factors, Algebra Represent. Theory. 2, 201–207, 1999.
There are 1 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Mathematics
Authors

Hongying Chen 0000-0002-1925-2158

Huang Juan 0000-0003-4447-5174

Tai Keun Kwak 0000-0001-6316-8650

Early Pub Date August 27, 2024
Publication Date
Submission Date January 4, 2024
Acceptance Date June 14, 2024
Published in Issue Year 2024 Early Access

Cite

APA Chen, H., Juan, H., & Kwak, T. K. (2024). On products of idempotents and nilpotents. Hacettepe Journal of Mathematics and Statistics1-15. https://doi.org/10.15672/hujms.1413424
AMA Chen H, Juan H, Kwak TK. On products of idempotents and nilpotents. Hacettepe Journal of Mathematics and Statistics. Published online August 1, 2024:1-15. doi:10.15672/hujms.1413424
Chicago Chen, Hongying, Huang Juan, and Tai Keun Kwak. “On Products of Idempotents and Nilpotents”. Hacettepe Journal of Mathematics and Statistics, August (August 2024), 1-15. https://doi.org/10.15672/hujms.1413424.
EndNote Chen H, Juan H, Kwak TK (August 1, 2024) On products of idempotents and nilpotents. Hacettepe Journal of Mathematics and Statistics 1–15.
IEEE H. Chen, H. Juan, and T. K. Kwak, “On products of idempotents and nilpotents”, Hacettepe Journal of Mathematics and Statistics, pp. 1–15, August 2024, doi: 10.15672/hujms.1413424.
ISNAD Chen, Hongying et al. “On Products of Idempotents and Nilpotents”. Hacettepe Journal of Mathematics and Statistics. August 2024. 1-15. https://doi.org/10.15672/hujms.1413424.
JAMA Chen H, Juan H, Kwak TK. On products of idempotents and nilpotents. Hacettepe Journal of Mathematics and Statistics. 2024;:1–15.
MLA Chen, Hongying et al. “On Products of Idempotents and Nilpotents”. Hacettepe Journal of Mathematics and Statistics, 2024, pp. 1-15, doi:10.15672/hujms.1413424.
Vancouver Chen H, Juan H, Kwak TK. On products of idempotents and nilpotents. Hacettepe Journal of Mathematics and Statistics. 2024:1-15.