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http://dx.doi.org/10.4134/BKMS.2014.51.6.1851

A NOTE ON ZERO DIVISORS IN w-NOETHERIAN-LIKE RINGS  

Kim, Hwankoo (School of Computer and Information Engineering Hoseo University)
Kwon, Tae In (Department of Mathematics Changwon National University)
Rhee, Min Surp (Department of Mathematics Dankook University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.6, 2014 , pp. 1851-1861 More about this Journal
Abstract
We introduce the concept of w-zero-divisor (w-ZD) rings and study its related rings. In particular it is shown that an integral domain R is an SM domain if and only if R is a w-locally Noetherian w-ZD ring and that a commutative ring R is w-Noetherian if and only if the polynomial ring in one indeterminate R[X] is a w-ZD ring. Finally we characterize universally zero divisor rings in terms of w-ZD modules.
Keywords
zero divisor; zero divisor ring; zero divisor module; universally zero divisor ring; w-operation;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 S. El Baghdadi, On a class of Prufer v-multiplication domains, Comm. Algebra 30 (2002), no. 8, 3723-3742.   DOI   ScienceOn
2 G. Fusacchia, Strong semistar Noetherian domains, Houston J. Math. 39 (2013), no. 1, 1-20.
3 R. Gilmer, Multiplicative Ideal Theory, Queen's Papers in Pure and Applied Mathematics, vol 90, Queen's University, Kingston, Ontario, 1992.
4 R. W. Gilmer and W. Heinzer, The Laskerian property, power series rings and Noetherian spectra, Proc. Amer. Math. Soc. 79 (1980), no. 1, 13-16.   DOI   ScienceOn
5 J. R. Hedstrom and E. G. Houston, Some remarks on star operations, J. Pure Appl. Algebra 18 (1980), no. 1, 37-44.   DOI   ScienceOn
6 W. Heinzer and D. Lantz, The Laskerian property in commutative rings, J. Algebra 101 (1981), no. 1, 101-114.
7 W. Heinzer and J. Ohm, Locally Noetherian commutative rings, Trans. Amer. Math. Soc. 158 (1971), no. 2, 273-284.   DOI   ScienceOn
8 W. Heinzer and J. Ohm, On the Noetherian-like rings of E. G. Evans, Proc. Amer. Math. Soc. 34 (1972), no. 1, 73-74.   DOI   ScienceOn
9 B. G. Kang, Prufer v-multiplication domains and the ring ${R[X]_N}_v$, J. Algebra 123 (1989), no. 1, 151-170.   DOI
10 I. Kaplansky, Commutative Rings, University of Chicago Press, Chicago 1974.
11 H. Kim, Module-theoretic characterizations of t-linkative domains, Comm. Algebra 36 (2008), no. 5, 1649-1670.   DOI   ScienceOn
12 E. G. Evans, Jr., Zero divisors in Noetherian-like rings, Trans. Amer. Math. Soc. 155 (1971), no. 2, 505-512.   DOI   ScienceOn
13 M. H. Park, Power series rings over strong Mori domains. J. Algebra 270 (2003), no. 1, 361-368.   DOI   ScienceOn
14 H. Kim and T. I. Kwon, Integral domains which are t-locally Noetherian, J. Chungcheong Math. Soc. 24 (2011), 843-848.
15 H. Kim and F. Wang, On ${\phi}$-strong Mori rings, Houston J. Math. 38 (2012), no. 2, 359-371.
16 F. Wang and R. L. McCasland, On w-modules over strong Mori domains, Comm. Algebra 25 (1997), no. 4, 1285-1306.   DOI   ScienceOn
17 S. Visweswaran, A note on universally zero-divisor rings. Bull. Austral. Math. Soc. 43 (1991), no. 2, 233-239.   DOI
18 F. Wang, Finitely presented type modules and w-coherent rings, J. Sichuan Normal Univ. 33 (2010), 1-9.
19 F. Wang and J. Zhang, Injective modules over w-Noetherian rings, Acta Math. Sinica (Chin. Ser.) 53 (2010), no. 6, 1119-1130.
20 L. Xie, F. Wang, and Y. Tian, On w-linked overrings, J. Math. Res. Exposition 31 (2011), no. 2, 337-346.
21 H. Yin, F. Wang, X. Zhu, and Y. Chen. w-Modules over commutative rings, J. Korean Math. Soc. 48 (2011), no. 1, 207-222.   과학기술학회마을   DOI   ScienceOn
22 S. El Baghdadi, H. Kim, and F. Wang, A note on generalized Krull domains, J. Algebra Appl. 13 (2014), no. 7, 1450029 (18 pp).