SavedAdd your journal

Journals / International Electronic Journal of Algebra / 2017 / Volume: 22 Issue: 22

Baer Group Rings with Involution

Anil Khairnar
B. N. Waphare
Pages
—
Publication Date
2017-07-11
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Chen       (for principally quasi-Baer and principally projective rings).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We prove that if a group ring $RG$ is a (quasi) Baer $*$-ring, then so is $R$, whereas converse is not true.       Sufficient conditions are given so that for some finite cyclic groups $G$,      if $R$ is (quasi-) Baer $*$-ring, then so is the group ring $RG$.      We prove that if the group ring $RG$ is a Baer $*$-ring, then so is $RH$ for every subgroup $H$ of $G$.      Also, we generalize results of Zhong Yi, Yiqiang Zhou (for (quasi-) Baer rings) and  L.
📊
Key Findings & Data:We prove that if a group ring $RG$ is a (quasi) Baer $*$-ring, then so is $R$, whereas converse is not true.       Sufficient conditions are given so that for some finite cyclic groups $G$,      if $R$ is (quasi-) Baer $*$-ring, then so is the group ring $RG$.      We prove that if the group ring $RG$ is a Baer $*$-ring, then so is $RH$ for every subgroup $H$ of $G$.      Also, we generalize results of Zhong Yi, Yiqiang Zhou (for (quasi-) Baer rings) and  L.
💡
Conclusion & Impact:Chen       (for principally quasi-Baer and principally projective rings).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Group ring · Baer $*$-ring

Abstract

We prove that if a group ring $RG$ is a (quasi) Baer $*$-ring, then so is $R$, whereas converse is not true.       Sufficient conditions are given so that for some finite cyclic groups $G$,      if $R$ is (quasi-) Baer $*$-ring, then so is the group ring $RG$.      We prove that if the group ring $RG$ is a Baer $*$-ring, then so is $RH$ for every subgroup $H$ of $G$.      Also, we generalize results of Zhong Yi, Yiqiang Zhou (for (quasi-) Baer rings) and  L. Zan, J. Chen       (for principally quasi-Baer and principally projective rings).

🔖

Cite This Article

Khairnar, A., Waphare, B. N. (2017). Baer Group Rings with Involution. International Electronic Journal of Algebra, Volume: 22 Issue: 22. https://doi.org/10.24330/ieja.325913

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. E. P. Armendariz, A note on extensions of Baer and p.p.-rings, J. Austral. Math. Soc., 18 (1974), 470-473.
  2. G. F. Birkenmeier, J. Y. Kim and J. K. Park, On polynomial extensions of principally quasi-Baer rings, Kyungpook Math. J., 40(2) (2000), 247-253.
  3. G. F. Birkenmeier, J. Y. Kim and J. K. Park, Principally quasi-Baer rings, Comm. Algebra, 29(2) (2001), 639-660.
  4. G. F. Birkenmeier, J. Y. Kim and J. K. Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra, 159(1) (2001), 25-42.
  5. G. F. Birkenmeier and J. K. Park, Triangular matrix representations of ring extensions, J. Algebra, 265(2) (2003), 457-477.
  6. W. E. Clark, Twisted matrix units semigroup algebras, Duke Math. J., 34(3) (1967), 417-423.
  7. N. J. Groenewald, A note on extensions of Baer and p.p.-rings, Publ. Inst. Math. (Beograd) (N.S.), 34(48) (1983), 71-72.
  8. Y. Hirano, On ordered monoid rings over a quasi-Baer ring, Comm. Algebra, 29(5) (2001), 2089-2095.
  9. I. Kaplansky, Rings of Operators, W. A. Benjamin, Inc., New York- Amsterdam, 1968.
  10. A. Khairnar and B. N. Waphare, Order properties of generalized projections, Linear Multilinear Algebra, 65(7) (2017), 1446-1461.
  11. B. N. Waphare and A. Khairnar, Semi-Baer modules, J. Algebra Appl., 14(10) (2015), 1550145 (12 pp).
  12. Z. Yi and Y. Zhou, Baer and quasi-Baer properties of group rings, J. Aust. Math. Soc., 83(2) (2007), 285-296.
  13. L. Zan and J. Chen, p.p. properties of group rings, Int. Electron. J. Algebra, 3 (2008), 117-124.
  14. L. Zan and J. Chen, Principally quasi-Baer properties of group rings, Studia Sci. Math. Hungar., 49(4) (2012), 454-465.