EQUIVALENT CONDITIONS FOR A NOETHERIAN MODULE

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Reza Ovlyaee-Sarmazdeh (Department of Pure Mathematics, Faculty of Mathematical Science, University of Guilan) ;
Zahra Ghaffari (Department of Pure Mathematics, Faculty of Mathematical Science, University of Guilan) ;
Kiana Mozhdehy (Department of pure mathematics, Faculty of Mathematical Science, University of Guilan)

In this paper, we present useful characterizations for Noetherian modules using the theory of prime submodules.

The authors would like to thank the referees for the helpful suggestions.

P. Jothilingam, Cohen's theorem and Eakin-Nagata theorem revisited, Comm. Algebra, 28 (2000), no 10, 4861-4866. https://doi.org/10.1080/00927870008827126
H. I. Karakas, On Noetherian modules, Metu J. Pure and Appl. Sci 5 (1972), no. 2, 165-168.
C. P. Lu, Prime Submodules of Modules, Comment. Math. Univ. St. Pauli, 33 (1984), no. 1, 61-69.
C. P. Lu, Spectra of modules,Comm. Algebra, 23 (1995), no 10, 3741-3752. https://doi.org/10.1080/00927879508825430
C. P. Lu, The Zariski topology on the prime spectrum of a module, Houston J. Math 25 (1999), no. 3, 417-432.
C. P. Lu, Saturations of submodules, Comm. Algebra, 31 (2003), no. 6, 2655-2673. https://doi.org/10.1081/AGB-120021886
C. P. Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math 33 (2007), no. 1, 125-143.
A. R. Naghipour, A simple proof of Cohen's theorem, Amer. Math. Monthly 112 (2005), no. 9, 825-826. https://doi.org/10.1080/00029890.2005.11920257
A. Parkash and S. Kour, On Cohen's theorem for modules, Indian J. Pure Appl. Math 52 (2021), no. 3, 869-871. https://doi.org/10.1007/s13226-021-00101-z
T. S. Shores and W. J. Lewis, Serial modules and endomorphism rings, Duke Math. J 41 (1974), 889-909.
P. F. Smith, Concerning a theorem of I. S. Cohen, Analele stiintifice ale Universitatii Ovidius Constanta, XIth National Conference of Algebra (Constanta, 1994), 160-167, National Conference of Algebra, 2014.