Version 1
: Received: 24 August 2021 / Approved: 26 August 2021 / Online: 26 August 2021 (09:57:50 CEST)
How to cite:
Melhem, A.; Bataineh, M.; Abu-Dawwas, R. Characterizations of Graded Rings Over Which Every Graded Semi-primary Ideal is Graded 1-absorbing Primary. Preprints2021, 2021080503. https://doi.org/10.20944/preprints202108.0503.v1
Melhem, A.; Bataineh, M.; Abu-Dawwas, R. Characterizations of Graded Rings Over Which Every Graded Semi-primary Ideal is Graded 1-absorbing Primary. Preprints 2021, 2021080503. https://doi.org/10.20944/preprints202108.0503.v1
Melhem, A.; Bataineh, M.; Abu-Dawwas, R. Characterizations of Graded Rings Over Which Every Graded Semi-primary Ideal is Graded 1-absorbing Primary. Preprints2021, 2021080503. https://doi.org/10.20944/preprints202108.0503.v1
APA Style
Melhem, A., Bataineh, M., & Abu-Dawwas, R. (2021). Characterizations of Graded Rings Over Which Every Graded Semi-primary Ideal is Graded 1-absorbing Primary. Preprints. https://doi.org/10.20944/preprints202108.0503.v1
Chicago/Turabian Style
Melhem, A., Malik Bataineh and Rashid Abu-Dawwas. 2021 "Characterizations of Graded Rings Over Which Every Graded Semi-primary Ideal is Graded 1-absorbing Primary" Preprints. https://doi.org/10.20944/preprints202108.0503.v1
Abstract
Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. Graded semi-primary and graded $1$-absorbing primary ideals have been investigated and examined by several authors as generalizations of graded primary ideals. However, these three concepts are different. In this article, we characterize graded rings over which every graded semi-primary ideal is graded $1$-absorbing primary and graded rings over which every graded $1$-absorbing primary ideal is graded primary.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
