대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제33권4호
  • /
  • Pages.1075-1082
  • /
  • 2018
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON U-GROUP RINGS

  • Osba, Emad Abu (Department of Mathematics School of Science The University of Jordan) ;
  • Al-Ezeh, Hasan (Department of Mathematics School of Science The University of Jordan) ;
  • Ghanem, Manal (Department of Mathematics School of Science The University of Jordan)
  • 투고 : 2017.09.20
  • 심사 : 2017.12.21
  • 발행 : 2018.10.31
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초록

Let R be a commutative ring, G be an Abelian group, and let RG be the group ring. We say that RG is a U-group ring if a is a unit in RG if and only if ${\epsilon}(a)$ is a unit in R. We show that RG is a U-group ring if and only if G is a p-group and $p{\in}J(R)$. We give some properties of U-group rings and investigate some properties of well known rings, such as Hermite rings and rings with stable range, in the presence of U-group rings.

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참고문헌

  1. D. D. Anderson and O. A. Al-Mallah, Commutative group rings that are presimplifiable or domainlike, J. Algebra Appl. 16 (2017), no. 1, 1750019, 9 pp.
  2. A. Y. M. Chin, A note on semilocal group rings, Czechoslovak Math. J. 52(127) (2002), no. 4, 749-755. https://doi.org/10.1023/B:CMAJ.0000027230.45445.09
  3. I. G. Connell, On the group ring, Canad. J. Math. 15 (1963), 650-685. https://doi.org/10.4153/CJM-1963-067-0
  4. F. E. A. Johnson, Stably free cancellation for abelian group rings, Arch. Math. (Basel) 102 (2014), no. 1, 7-10. https://doi.org/10.1007/s00013-013-0599-8
  5. A. Klappeneckera and M. Holschneider, A Unified view on filter banks, Wavelet Appli- cations in Signal and Image Processing VI (Laine A. F., Unser M. A., Aldroubi A.), SPIE 3458, 2-13, 1998.
  6. T. Y. Lam, A crash course on stable range, cancellation, substitution and exchange, J. Algebra Appl. 3 (2004), no. 3, 301-343. https://doi.org/10.1142/S0219498804000897
  7. T. Y. Lam, Serre's Problem on Projective Modules, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2006.
  8. O. Lezama and C. Gallego, d-Hermite rings and skew PBW extensions, Sao Paulo J. Math. Sci. 10 (2016), no. 1, 60-72. https://doi.org/10.1007/s40863-015-0010-8
  9. W. K. Nicholson, Local group rings, Canad. Math. Bull. 15 (1972), 137-138. https://doi.org/10.4153/CMB-1972-025-1
  10. X. Wang and H. You, Cleanness of the group ring of an abelian p-group over a commutative ring, Algebra Colloq. 19 (2012), no. 3, 539-544. https://doi.org/10.1142/S1005386712000405