JOURNAL BROWSE
Search
Advanced SearchSearch Tips
SOME EXAMPLES OF QUASI-ARMENDARIZ RINGS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
SOME EXAMPLES OF QUASI-ARMENDARIZ RINGS
Hashemi, Ebrahim;
  PDF(new window)
 Abstract
In [12], McCoy proved that if R is a commutative ring, then whenever g(x) is a zero-divisor in R[x], there exists a nonzero c R such that cg(x) = 0. In this paper, first we extend this result to monoid rings. Then for a monoid M, we give some examples of M-quasi-Armendariz rings which are a generalization of quasi-Armendariz rings. Every reduced ring is M-quasi-Armendariz for any unique product monoid M and any strictly totally ordered monoid . Also is M-quasi-Armendariz when R is reduced and M-Armendariz.
 Keywords
Armendariz rings;quasi-Armendariz rings;monoid rings;unique product monoid rings;
 Language
English
 Cited by
 References
1.
E. P. Armendariz, A note on extensions of Baer and p.p.-rings, J. Austral. Math. Soc. 18 (1974), 470-473 crossref(new window)

2.
D. D. Anderson and S. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 73 (1997), 14-17

3.
G. F. Birkenmeier and J. K. Park, Triangular matrix representations of ring extensions, J. Algebra 265 (2003), no. 2, 103-122

4.
G. F Birkenmeier, J. Y. Kim, and J. K. Park, Polynomial extensions of Baer and quasi- Baer rings, J. Pure Appl. Algebra 159 (2001), no. 1, 25-42 crossref(new window)

5.
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)

6.
Y. Hirano, On ordered monoid rings over a quasi-Baer ring, Comm. Algebra 29 (2001), no. 5, 2089-2095 crossref(new window)

7.
C. Y. Hong, N. K. Kim, and T. K. Kwak, On skew Armendariz rings, Comm. Algebra 31 (2003), no. 1, 103-122 crossref(new window)

8.
C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751-761 crossref(new window)

9.
N. H Kim and Y. Lee, Armendariz rings and reduced rings. J. Algebra 223 (2000), no. 2, 477-488 crossref(new window)

10.
J. Krempa, Some examples of reduced rings, Algebra Colloq. 3 (1996), no. 4, 289-300

11.
T. K. Lee and T. L. Wong, On Armendariz rings, Houston J. Math. 29 (2003), no. 3, 583-593

12.
N. H. McCoy, Remarks on divisors of zero, Amer. Math. Monthly 49 (1942), 286-296 crossref(new window)

13.
J. Okninski, Semigroup Algebra, Monographs and Textbooks in Pure and Applied Mathematics, 138. Marcel Dekker, Inc., New York, 1991

14.
D. S. Passman, The Algebraic structure of group rings, Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1977

15.
M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), no. 1, 14-17

16.
P. Ribenboim, Noetherian rings of generalized power series, J. Pure Appl. Algebra 79 (1992), no. 3, 293-312 crossref(new window)

17.
L. Zhongkui, Armendariz rings relative to a monoid, Comm. Algebra 33 (2005), no. 3, 649-661 crossref(new window)