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Raplang Nongsiej1
Section:Research Paper, Product Type: Journal-Paper
Vol.6 ,
Issue.4 , pp.113-117, Aug-2019
CrossRef-DOI: https://doi.org/10.26438/ijsrmss/v6i4.113117
Online published on Aug 31, 2019
Copyright © Raplang Nongsiej . 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.
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IEEE Style Citation: Raplang Nongsiej, “Weak X-essential Ideals,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.113-117, 2019.
MLA Style Citation: Raplang Nongsiej "Weak X-essential Ideals." International Journal of Scientific Research in Mathematical and Statistical Sciences 6.4 (2019): 113-117.
APA Style Citation: Raplang Nongsiej, (2019). Weak X-essential Ideals. International Journal of Scientific Research in Mathematical and Statistical Sciences, 6(4), 113-117.
BibTex Style Citation:
@article{Nongsiej_2019,
author = {Raplang Nongsiej},
title = {Weak X-essential Ideals},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {8 2019},
volume = {6},
Issue = {4},
month = {8},
year = {2019},
issn = {2347-2693},
pages = {113-117},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1473},
doi = {https://doi.org/10.26438/ijcse/v6i4.113117}
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v6i4.113117}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=1473
TI - Weak X-essential Ideals
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Raplang Nongsiej
PY - 2019
DA - 2019/08/31
PB - IJCSE, Indore, INDIA
SP - 113-117
IS - 4
VL - 6
SN - 2347-2693
ER -
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Abstract :
Weak X-essential ideals are introduced in this paper which are generalizations of essential ideals and X-essential ideals. Some properties of weak X-essential ideals are investigated. In particular, we proved that the property of weak X-essential is preserved under finite intersection, inverse image and factor rings. We also found out conditions on Noetherian rings which ensure that direct sums of weak X-essential ideals are weak essential ideals and vice versa.
Key-Words / Index Term :
essential submodule, X-essential submodule, weak X-essential ideal
References :
[1] R.E. Johnson: “Structure Theory of Faithful Rings”, Proc. Amer. Math. Soc. 2(1951), 891-895.
[2] B. Eckmann and A. Schopf, “Uber Injective Moduln”, Archiv der Math 4(1953), 75-78.
[3] F. W. Anderson and K.R. Fuller : “Rings and Categories of Modules (Graduate Text in Mathematics 13)”, Springer -Verlag, Berlin Heldelberg-New York, (1974).
[4] S. Safaeenyan and N. Saboori Shirazi: “Essential Submodules with respect to an Arbitrary Submodule”, Journal of Mathematical Extension, Vol. 7 No. 3, (2013), 15-27.
[5] M. F. Atiyah and I. G. Macdonald: “Introduction to Commutative Algebras”, Addison Wesley, (1972).
[6] K. R. Goodearl, R. B. Warfield, Jr: “An Introduction to Non commutative Noetherian Rings Second Edition”, (1989).
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