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SKEW LAURENT POLYNOMIAL EXTENSIONS OF BAER AND P.P.-RINGS
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 Title & Authors
SKEW LAURENT POLYNOMIAL EXTENSIONS OF BAER AND P.P.-RINGS
Nasr-Isfahani, Alireza R.; Moussavi, Ahmad;
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 Abstract
Let R be a ring and a monomorphism of R. We study the skew Laurent polynomial rings R[x, x; ] over an -skew Armendariz ring R. We show that, if R is an -skew Armendariz ring, then R is a Baer (resp. p.p.-)ring if and only if R[x, x; ] is a Baer (resp. p.p.-) ring. Consequently, if R is an Armendariz ring, then R is a Baer (resp. p.p.-)ring if and only if R[x, x] is a Baer (resp. p.p.-)ring.
 Keywords
skew Laurent polynomial rings;Baer rings;p.p.-rings;-rigid rings;skew-Armendariz rings;
 Language
English
 Cited by
1.
INSERTION-OF-FACTORS-PROPERTY ON SKEW POLYNOMIAL RINGS,;;;;;

대한수학회지, 2015. vol.52. 6, pp.1161-1178 crossref(new window)
1.
Baer and Quasi-Baer Properties of Skew Generalized Power Series Rings, Communications in Algebra, 2016, 44, 4, 1615  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.
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.
E. P. Armendariz, H. K. Koo, and J. K. Park, Isomorphic Ore extensions, Comm. Algebra 15 (1987), no. 12, 2633–2652. crossref(new window)

4.
G. F. Birkenmeier, J. Y. Kim, and J. K. Park, Principally quasi-Baer rings, Comm. Algebra 29 (2001), no. 2, 639–660. crossref(new window)

5.
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)

6.
G. F. Birkenmeier, J. Y. Kim, and J. K. Park, On polynomial extensions of principally quasi-Baer rings, Kyungpook Math. J. 40 (2000), no. 2, 247-253.

7.
E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta Math. Hungar. 107 (2005), no. 3, 207-224 crossref(new window)

8.
Y. Hirano, On isomorphisms between Ore extensions, Preprint

9.
Y. Hirano, On the uniqueness of rings of coefficients in skew polynomial rings, Publ. Math. Debrecen 54 (1999), no. 3-4, 489-495.

10.
C. Y. Hong, N. K. Kim, and T. Kwak, Ore extensions of Baer and p.p.-rings, J. Pure Appl. Algebra 151 (2000), no. 3, 215-226 crossref(new window)

11.
C. Y. Hong, N. K. Kim, and T. Kwak, On skew Armendariz rings, Comm. Algebra 31 (2003), no. 1, 103–122. crossref(new window)

12.
C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751-761 crossref(new window)

13.
D. A. Jordan, Bijective extensions of injective ring endomorphisms, J. London Math. Soc. (2) 25 (1982), no. 3, 435-448 crossref(new window)

14.
I. Kaplansky, Rings of Operators, W. A. Benjamin, Inc., New York-Amsterdam, 1968

15.
N. K. Kim and Y. Lee, Armendariz rings and reduced rings, J. Algebra 223 (2000), no. 2, 477-488 crossref(new window)

16.
J. Krempa, Some examples of reduced rings, Algebra Colloq. 3 (1996), no. 4, 289-300.

17.
T. K. Lee and T. L. Wong, On Armendariz rings, Houston J. Math. 29 (2003), no. 3, 583-593.

18.
J. Matczuk, A characterization of $\sigma$-rigid rings, Comm. Algebra 32 (2004), no. 11, 4333-4336 crossref(new window)

19.
A. Moussavi and E. Hashemi, Semiprime skew polynomial rings, Sci. Math. Jpn. 64 (2006), no. 1, 91-95.

20.
M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), no. 1, 14-17. crossref(new window)