JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON ANNIHILATOR IDEALS OF A NEARRING OF SKEW POLYNOMIALS OVER A RING
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON ANNIHILATOR IDEALS OF A NEARRING OF SKEW POLYNOMIALS OVER A RING
Hashemi, Ebrahim;
  PDF(new window)
 Abstract
For a ring endomorphism and an of a ring R, we study relation between the set of annihilators in R and the set of annihilators in nearring . Also we extend results of Armendariz on the Baer and p.p. conditions in a polynomial ring to certain analogous annihilator conditions in a nearring of skew polynomials. These results are somewhat surprising since, in contrast to the skew polynomial ring and skew power series case, the nearring of skew polynomials and skew power series have substitution for its "multiplication" operation.
 Keywords
annihilator conditions;nearrings;skew power series;skew polynomial rings;Baer ring;quasi-Baer rings; rings;Rickart rings;
 Language
English
 Cited by
 References
1.
D. D. Anderson and V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 26 (1998), no. 7, 2265-2275 crossref(new window)

2.
E. P. Armendariz, A note on extensions of Baer and P.P.-rings, J. Austral. Math. Soc. 18 (1974), 470-473 crossref(new window)

3.
S. K. Berberian , Baer $\ast-rings$, Springer-Verlag, Berlin, 1972

4.
G. F. Birkenmeier and F. K. Huang, Annihilator conditions on polynomials, Comm.Algebra 29 (2001), no. 5, 2097-2112 crossref(new window)

5.
G. F. Birkenmeier and F. K. Huang, Annihilator conditions on formal power series, Algebra colloq. 9 (2002), no. 1, 29-37

6.
G. F. Birkenmeier and F. K. Huang, Annihilator conditions on polynomials II, Monatsh. Math. 141 (2004), no. 4, 265-276 crossref(new window)

7.
G. F. Birkenmeier, J. Y. Kim, and J. K. Park, Quasi-Baer ring extensions and biregular rings, Bull. Austral. Math. Soc. 61 (2000), no. 1, 39-52 crossref(new window)

8.
G. F. Birkenmeier, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra 159 (2001), no. 1, 25-42 crossref(new window)

9.
G. F. Birkenmeier, Principally quasi-Baer rings, Comm. Algebra 29 (2001), no. 2, 639-660 crossref(new window)

10.
W. E. Clark, Twisted matrix units semigroup algebra, Duke Math. J. 34 (1967), 417- 423 crossref(new window)

11.
J. A. Fraser and W. K. Nicholson, Reduced PP-rings, Math. Japon. 34 (1989), no. 5, 715-725

12.
E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta Math. Hungar. 107 (2005), no. 3, 207-224 crossref(new window)

13.
E. Hashemi and A. Moussavi, Skew power series extensions of $\alpha-rigid$ p.p.-rings, Bull. Korean Math. Soc. 41 (2004), no. 4, 657-665 crossref(new window)

14.
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)

15.
C. Y. Hong , N. K. Kim, and T. K. Kwak, Ore extensions of Baer and p.p.-rings, J. Pure Appl. Algebra 151 (2000), 215-226 crossref(new window)

16.
I. Kaplansky, Rings of operators, Benjamin, New York, 1968

17.
J. Krempa, Some examples of reduced rings, Algebra Colloq. 3 (1996), no. 4, 289-300

18.
A. Moussavi and E. Hashemi, On $(\alpha,\;\delta)$ Skew Armendariz rings, J. Korean Math. Soc. 42 (2005), no. 2, 353-363 crossref(new window)