Browse > Article
http://dx.doi.org/10.4134/BKMS.2004.41.4.657

SKEW POWER SERIES EXTENSIONS OF α-RIGID P.P.-RINGS  

Hashemi, Ebrahim (Department of Mathematics, University of Tarbiat Modarres)
Moussavi, Ahmad (Department of Mathematics, University of Tarbiat Modarres)
Publication Information
Bulletin of the Korean Mathematical Society / v.41, no.4, 2004 , pp. 657-664 More about this Journal
Abstract
We investigate skew power series of $\alpha$-rigid p.p.-rings, where $\alpha$ is an endomorphism of a ring R which is not assumed to be surjective. For an $\alpha$-rigid ring R, R[[${\chi};{\alpha}$]] is right p.p., if and only if R[[${\chi},{\chi}^{-1};{\alpha}$]] is right p.p., if and only if R is right p.p. and any countable family of idempotents in R has a join in I(R).
Keywords
Baer rings; right p.p.-rings; $\alpha$-rigid rings; skew power eries; Ore extensions;
Citations & Related Records
연도 인용수 순위
  • Reference
1 G. F. Birkenmeier, On polynomial extensions of principally quasi-Baer rings, Kyungpook Math. J. 40 (2000), 247–253
2 J. A. Fraser and W. K. Nicholson, Reduced PP-rings, Math. Japonica 34 (1989), no. 5, 715–725
3 Y. Hirano, On annihilator ideals of a polynomial ring over a noncommutative ring, J. Pure Appl. Algebra 168 (2002), 45–52
4 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
5 C. Y. Hong, N. K. Kim and T. K. Kwak, On skew Armendariz rings, Comm. Algebra 31 (2003), no. 1, 103–122
6 C. Huh, Y. Lee and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751–761
7 G. F. Birkenmeier, J. Y. Kim and J. K. Park, Principally quasi-Baer rings, Comm. Algebra 29 (2001), no. 2, 639–660
8 D. D. Anderson and V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 26 (1998), no. 7, 2265–2275   DOI   ScienceOn
9 E. P. Armendariz, A note on extensions of Baer and p.p.-rings, J. Aust. Math. Soc. 18 (1974), 470–473
10 G. F. Birkenmeier, Idempotents and completely semiprime ideals, Comm. Algebra 11 (1983), 567–580
11 G. F. Birkenmeier, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra 159 (2001), 24–42
12 D. A. Jordan, Bijective extension of injective ring endomorphisms, J. London Math. Soc. 35 (1982), no. 2, 435–488
13 I. Kaplansky, Rings of Operators, Benjamin, New York, 1965
14 A. Moussavi and E. Hashemi, Semiprime skew polynomial rings, submitted
15 N. H. Kim and Y. Lee, Armendariz rings and reduced rings, J. Algebra 223 (2000), 477–488
16 J. Krempa, Some examples of reduced rings, Algebra Colloq. 3 (1996), no. 4, 289–300
17 Z. Liu, A note on principally quasi-Baer rings, Comm. Algebra 30 (2002), no. 8, 3885–3890
18 M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), 14–17
19 C. E. Rickart, Banach algebras with an adjoint operation, Ann. of Math. 47 (1946), 528–550