On Locally Artinian Rings

Authors

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

DOI:

https://doi.org/10.17656/jzs.10600

Keywords:

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

Abstract

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.

References

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Published

2017-03-20

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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