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ON φ-VON NEUMANN REGULAR RINGS
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 Title & Authors
ON φ-VON NEUMANN REGULAR RINGS
Zhao, Wei; Wang, Fanggui; Tang, Gaohua;
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 Abstract
Let R be a commutative ring with and let = {R|R is a commutative ring and Nil(R) is a divided prime ideal}. If , then R is called a -ring. In this paper, we introduce the concepts of -torsion modules, -flat modules, and -von Neumann regular rings.
 Keywords
-torsion modules;-flat modules;-von Neumann regular rings;
 Language
English
 Cited by
1.
Nonnil-coherent rings, Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2016, 57, 2, 297  crossref(new windwow)
 References
1.
D. F. Anderson and A. Badawi, On ${\phi}$-Prufer rings and -Bezout rings, Houston J. Math. 30 (2004), no. 2, 331-343.

2.
D. F. Anderson and A. Badawi, on ${\phi}$-Dedekind rings and ${\phi}$-Krull rings, Houston J. Math. 31 (2005), no. 4, 1007-1022.

3.
A. Badawi, On divided commutative rings, Comm. Algebra 27 (1999), no. 3, 1465-1474. crossref(new window)

4.
A. Badawi, On ${\phi}$-pseudo-valuation rings, Advances in commutative ring theory (Fez, 1997), 101-110, Lecture Notes in Pure and Appl. Math., 205, Dekker, New York, 1999.

5.
A. Badawi, On ${\phi}$-pseudo-valuation rings. II, Houston J. Math. 26 (2000), no. 3, 473-480.

6.
A. Badawi, On ${\phi}$-chained rings and -pseudo-valuation rings, Houston J. Math. 27 (2001), no. 4, 725-736.

7.
A. Badawi, On divided rings and ${\phi}$-pseudo-valuation rings, Commutative rings, 5-14, Nova Sci. Publ., Hauppauge, NY, 2002.

8.
A. Badawi, On Nonnil-Noetherian rings, Comm. Algebra 31 (2003), no. 4, 1669-1677. crossref(new window)

9.
A. Badawi, Factoring nonnil ideals as a product of prime and invertible ideals, Bulletin of the London Matth. Society 37 (2005), 665-672. crossref(new window)

10.
A. Badawi, On rings with divided nil ideal: a survey, Commutative algebra and its applications, 21-40, Walter de Gruyter, Berlin, 2009.

11.
A. Badawi and D. E. Dobbs, Strong ring extensions and ${\phi}$-pseudo-valuation rings, Houston J. Math. 32 (2006), no. 2, 379-398.

12.
A. Badawi and A. Jaballah, Some finiteness conditions on the set of overrings of a ${\phi}$-ring, Houston J. Math. 34 (2008), no. 2, 397-408.

13.
A. Badawi and T. G. Lucas, Rings with prime nilradical, in Arithmetical Properties of Commutative Rings and Monoids, vol. 241 of Lect. Notes Pure Appl. Math., pp. 198-212, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2005.

14.
A. Badawi and T. G. Lucas, on ${\phi}$-Mori rings, Houston J. Math. 32 (2006), no. 1, 1-32.

15.
D. E. Dobbs, Divided rings and going-down, Pacific J. Math. 67 (1976), no. 2, 353-363. crossref(new window)

16.
S. Hizem and A. Benhissi, Nonnil-Noetherian rings and the SFT property, Rocky Moun-tain J. Math. 41 (2011), no. 5, 1483-1500. crossref(new window)

17.
J. A. Huckaba, Commutative Rings with Zero Divisors, Marcel Dekker, New York/Basel, 1988.

18.
H. Kim and F. G. Wang, On ${\phi}$-strong Mori rings, Houston J. Math. 38 (2012), no. 2, 359-371.

19.
C. Lomp and A. Sant'ana, Comparability, distributivity and non-commutative -rings, Groups, rings and group rings, 205-217, Contemp. Math., 499, Amer. Math. Soc., Providence, RI, 2009.

20.
F. G. Wang, Commutative Rings and Star-Operation Theory, Sicence Press, Beijing, 2006.