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SPECIAL WEAK PROPERTIES OF GENERALIZED POWER SERIES RINGS
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 Title & Authors
SPECIAL WEAK PROPERTIES OF GENERALIZED POWER SERIES RINGS
Ouyang, Lunqun;
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 Abstract
Let be a ring and the set of all nilpotent elements of . For a subset of a ring , we define for all }, which is called a weak annihilator of in . ring is called weak zip provided that for any subset of , if , then there exists a finite subset such that , and a ring is called weak symmetric if for all a, b, . It is shown that a generalized power series ring is weak zip (resp. weak symmetric) if and only if is weak zip (resp. weak symmetric) under some additional conditions. Also we describe all weak associated primes of the generalized power series ring in terms of all weak associated primes of in a very straightforward way.
 Keywords
weak annihilator;weak associated prime;generalized power series;
 Language
English
 Cited by
1.
McCoy property and nilpotent elements of skew generalized power series rings, Journal of Algebra and Its Applications, 2017, 16, 10, 1750183  crossref(new windwow)
2.
Nilpotent elements and nil-Armendariz property of skew generalized power series rings, Asian-European Journal of Mathematics, 2017, 10, 02, 1750034  crossref(new windwow)
 References
1.
D. D. Anderson and V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 26 (1998), no. 7, 2265-2272. crossref(new window)

2.
S. Annin, Associated primes over skew polynomial rings, Comm. Algebra 30 (2002), no. 5, 2511-2528. crossref(new window)

3.
S. Annin, Associated primes over Ore extension rings, J. Algebra Appl. 3 (2004), no. 2, 193-205. crossref(new window)

4.
J. A. Beachy and W. D. Blair, Rings whose faithful left ideals are cofaithful, Pacific J. Math. 58 (1975), no. 1, 1-13. crossref(new window)

5.
J. Brewer and W. Heinzer, Associated primes of principal ideals, Duke Math. J. 41 (1974), 1-7. crossref(new window)

6.
G. A. Elliott and P. Ribenboim, Fields of generalized power series, Arch. Math. (Basel) 54 (1990), no. 4, 365-371. crossref(new window)

7.
C. Faith, Associated primes in commutative polynomial rings, Comm. Algebra 28 (2000), no. 8, 3983-3986. crossref(new window)

8.
Y. Hirano, On annihilator ideals of a polynomial ring over a noncommutative ring, J. Pure Appl. Algebra 168 (2002), no. 1, 45-52. crossref(new window)

9.
C. Y. Hong, N. K. Kim, T. K. Kwak, and Y. Lee, Extensions of zip rings, J. Pure Appl. Algebra 195 (2005), no. 3, 231-242. crossref(new window)

10.
J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull. 14 (1971), 359-368. crossref(new window)

11.
Z. Liu, PF-rings of generalised power series, Bull. Austral. Math. Soc. 57 (1998), no. 3, 427-432. crossref(new window)

12.
Z. Liu, Injectivity of modules of generalized inverse polynomials, Comm. Algebra 29 (2001), no. 2, 583-592. crossref(new window)

13.
Z. Liu, Special properties of rings of generalized power series, Comm. Algebra 32 (2004), no. 8, 3215-3226. crossref(new window)

14.
G. Marks, On 2-primal Ore extensions, Comm. Algebra 29 (2001), no. 5, 2113-2123. crossref(new window)

15.
L. Ouyang, Ore extensions of weak zip rings, Glasg. Math. J. 51 (2009), no. 3, 525-537. crossref(new window)

16.
L. Ouyang and Y. Chen, On weak symmetric rings, Comm. Algebra 38 (2010), no. 2, 697-713. crossref(new window)

17.
P. Ribenboim, Rings of generalized power series: Nilpotent elements, Abh. Math. Sem. Univ. Hamburg 61 (1991), 15-33. crossref(new window)

18.
P. Ribenboim, Noetherian rings of generalized power series, J. Pure. Appl. Algebra 79 (1992), no. 3, 293-312. crossref(new window)

19.
P. Ribenboim, Semisimple rings and von Neumann regular rings of generalized power series, J. Algebra 198 (1997), no. 2, 327-338. crossref(new window)

20.
R. C. Shock, Polynomial rings over finite dimensional rings, Pacific J. Math. 42 (1972), 251-257. crossref(new window)