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Year 2018, , 129 - 152, 05.07.2018
https://doi.org/10.24330/ieja.440241

Abstract

References

  • A. Badawi, On abelian pi-regular rings, Comm. Algebra, 25(4) (1997), 1009- 1021.
  • M. Baser, A. Harmanci and T. K. Kwak, Generalized semicommutative rings and their extensions, Bull. Korean Math. Soc., 45(2) (2008), 285-297.
  • M. Baser and T. K. Kwak, Extended semicommutative rings, Algebra Colloq., 17(2) (2010), 257-264.
  • H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc., 2 (1970), 363-368.
  • A. Y. M. Chin, Clean elements in abelian rings, Proc. Indian Acad. Sci. Math. Sci., 119(2) (2009), 145-148.
  • P. M. Cohn, Reversible rings, Bull. London Math. Soc., 31(6) (1999), 641-648. [7] G. Ehrlich, Unit-regular rings, Portugal. Math., 27 (1968), 209-212.
  • M. Henriksen, Two classes of rings generated by their units, J. Algebra, 31 (1974), 182-193.
  • S. U. Hwang, Y. C. Jeon and K. S. Park, On NCI rings, Bull. Korean Math. Soc., 44(2) (2007), 215-223.
  • N. K. Kim, S. B. Nam and J. Y. Kim, On simple singular GP-injective modules, Comm. Algebra, 27(5) (1999), 2087-2096.
  • J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull., 14 (1971), 359-368.
  • R. Mohammadi, A. Moussavi and M. Zahiri, On nil-semicommutative rings, Int. Electron. J. Algebra, 11 (2012), 20-37.
  • W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229 (1977), 269-278.
  • W. K. Nicholson and M. F. Yousif, Mininjective rings, J. Algebra, 187(2) (1997), 548-578.
  • G. Y. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc., 184 (1973), 43-60.
  • L. N. Vaserstein, Bass's rst stable range condition, J. Pure Appl. Algebra, 34(2-3) (1984), 319-330.
  • J. C. Wei, On simple singular Y J-injective modules, Southeast Asian Bull. Math., 31(5) (2007), 1009-1018.
  • J. C. Wei, Certain rings whose simple singular modules are nil-injective, Tur- kish J. Math., 32(4) (2008), 393-408.
  • J. C. Wei and J. H. Chen, Nil-injective rings, Int. Electron. J. Algebra, 2 (2007), 1-21.
  • J. C. Wei and L. B. Li, Strong DS rings, Southeast Asian Bull. Math., 33(2) (2009), 375-390.
  • J. C. Wei and L. B. Li, Quasi-normal rings, Comm. Algebra, 38(5) (2010), 1855-1868. J. C. Wei and Y. C. Qu, On rings containing a non-essential nil-injective maximal left ideal, Kyungpook Math. J., 52(2) (2012), 179-188.
  • T. S. Wu and P. Chen, On nitely generated projective modules and exchange rings, Algebra Colloq., 9(4) (2002), 433-444.
  • H.-P. Yu, On quasi-duo rings, Glasgow Math. J., 37(1) (1995), 21-31.
  • H.-P. Yu, Stable range one for exchange rings, J. Pure Appl. Algebra, 98(1) (1995), 105-109.

SOME STUDIES ON GZI RINGS

Year 2018, , 129 - 152, 05.07.2018
https://doi.org/10.24330/ieja.440241

Abstract

A ring R is called generalized ZI (or GZI for short) if for any
a 2 N(R) and b 2 R, ab = 0 implies aRba = 0, which is a proper generalization
of ZI rings. In this paper, many properties of GZI rings are introduced, some
known results are extended. Further, we introduce generalized GZI rings
as a generalization of GZI rings, and quasi-abel rings as a generalization of
generalized GZI rings. Some important results on Abel rings are extended to
generalized GZI rings and quasi-abel rings.

References

  • A. Badawi, On abelian pi-regular rings, Comm. Algebra, 25(4) (1997), 1009- 1021.
  • M. Baser, A. Harmanci and T. K. Kwak, Generalized semicommutative rings and their extensions, Bull. Korean Math. Soc., 45(2) (2008), 285-297.
  • M. Baser and T. K. Kwak, Extended semicommutative rings, Algebra Colloq., 17(2) (2010), 257-264.
  • H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc., 2 (1970), 363-368.
  • A. Y. M. Chin, Clean elements in abelian rings, Proc. Indian Acad. Sci. Math. Sci., 119(2) (2009), 145-148.
  • P. M. Cohn, Reversible rings, Bull. London Math. Soc., 31(6) (1999), 641-648. [7] G. Ehrlich, Unit-regular rings, Portugal. Math., 27 (1968), 209-212.
  • M. Henriksen, Two classes of rings generated by their units, J. Algebra, 31 (1974), 182-193.
  • S. U. Hwang, Y. C. Jeon and K. S. Park, On NCI rings, Bull. Korean Math. Soc., 44(2) (2007), 215-223.
  • N. K. Kim, S. B. Nam and J. Y. Kim, On simple singular GP-injective modules, Comm. Algebra, 27(5) (1999), 2087-2096.
  • J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull., 14 (1971), 359-368.
  • R. Mohammadi, A. Moussavi and M. Zahiri, On nil-semicommutative rings, Int. Electron. J. Algebra, 11 (2012), 20-37.
  • W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229 (1977), 269-278.
  • W. K. Nicholson and M. F. Yousif, Mininjective rings, J. Algebra, 187(2) (1997), 548-578.
  • G. Y. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc., 184 (1973), 43-60.
  • L. N. Vaserstein, Bass's rst stable range condition, J. Pure Appl. Algebra, 34(2-3) (1984), 319-330.
  • J. C. Wei, On simple singular Y J-injective modules, Southeast Asian Bull. Math., 31(5) (2007), 1009-1018.
  • J. C. Wei, Certain rings whose simple singular modules are nil-injective, Tur- kish J. Math., 32(4) (2008), 393-408.
  • J. C. Wei and J. H. Chen, Nil-injective rings, Int. Electron. J. Algebra, 2 (2007), 1-21.
  • J. C. Wei and L. B. Li, Strong DS rings, Southeast Asian Bull. Math., 33(2) (2009), 375-390.
  • J. C. Wei and L. B. Li, Quasi-normal rings, Comm. Algebra, 38(5) (2010), 1855-1868. J. C. Wei and Y. C. Qu, On rings containing a non-essential nil-injective maximal left ideal, Kyungpook Math. J., 52(2) (2012), 179-188.
  • T. S. Wu and P. Chen, On nitely generated projective modules and exchange rings, Algebra Colloq., 9(4) (2002), 433-444.
  • H.-P. Yu, On quasi-duo rings, Glasgow Math. J., 37(1) (1995), 21-31.
  • H.-P. Yu, Stable range one for exchange rings, J. Pure Appl. Algebra, 98(1) (1995), 105-109.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Yinchun Qu This is me

Junchao Wei

Publication Date July 5, 2018
Published in Issue Year 2018

Cite

APA Qu, Y., & Wei, J. (2018). SOME STUDIES ON GZI RINGS. International Electronic Journal of Algebra, 24(24), 129-152. https://doi.org/10.24330/ieja.440241
AMA Qu Y, Wei J. SOME STUDIES ON GZI RINGS. IEJA. July 2018;24(24):129-152. doi:10.24330/ieja.440241
Chicago Qu, Yinchun, and Junchao Wei. “SOME STUDIES ON GZI RINGS”. International Electronic Journal of Algebra 24, no. 24 (July 2018): 129-52. https://doi.org/10.24330/ieja.440241.
EndNote Qu Y, Wei J (July 1, 2018) SOME STUDIES ON GZI RINGS. International Electronic Journal of Algebra 24 24 129–152.
IEEE Y. Qu and J. Wei, “SOME STUDIES ON GZI RINGS”, IEJA, vol. 24, no. 24, pp. 129–152, 2018, doi: 10.24330/ieja.440241.
ISNAD Qu, Yinchun - Wei, Junchao. “SOME STUDIES ON GZI RINGS”. International Electronic Journal of Algebra 24/24 (July 2018), 129-152. https://doi.org/10.24330/ieja.440241.
JAMA Qu Y, Wei J. SOME STUDIES ON GZI RINGS. IEJA. 2018;24:129–152.
MLA Qu, Yinchun and Junchao Wei. “SOME STUDIES ON GZI RINGS”. International Electronic Journal of Algebra, vol. 24, no. 24, 2018, pp. 129-52, doi:10.24330/ieja.440241.
Vancouver Qu Y, Wei J. SOME STUDIES ON GZI RINGS. IEJA. 2018;24(24):129-52.