On Locally Artinian Rings


  • Adil Kadir Jabbar Department of Mathematics, Faculty of Science and Science Education, School of Science, University of Sulaimani, Kurdistan Region, Iraq. Author




Artinian rings, Locally Artinian rings, Noetherian rings, Locally Noetherian rings and Nakayama's Lemma


In this paper, a new ring is introduced and studied, which we call a locally Artinian ring and it is a generalization of an Artinian ring. Several properties of Artinian rings are extended to this new type of commutative rings. Some conditions are given under which a locally Artinian ring is Artinian. It is known that, a locally Artinian ring is locally Noetherian, but the converse is not true and an example of a locally Noetherian ring which is not locally Artinian is given. Furthermore, a necessary and sufficient condition is given for a locally Noetherian ring to be locally Artinian.


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How to Cite

On Locally Artinian Rings. (2017). Journal of Zankoy Sulaimani - Part A, 19(1), 227-232. https://doi.org/10.17656/jzs.10600

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