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EXTENSIONS OF Σ-ZIP RINGS

Year 2017, , 1 - 22, 17.01.2017
https://doi.org/10.24330/ieja.295657

Abstract

t. In this note we consider a new concept, so called Σ-zip ring, which
unifies zip rings and weak zip rings. We observe the basic properties of Σ-zip
rings, constructing typical examples. We study the relationship between the
Σ-zip property of a ring R and that of its Ore extensions and skew generalized
power series extensions. As a consequence, we obtain a generalization of several
known results relating to zip rings and weak zip rings. 

References

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  • Math. Hungar., 107(3) (2005), 207-224.
  • [6] C. Y. Hong, N. K. Kim, T. K. Kwak and Y. Lee, Extensions of zip rings, J.
  • Pure Appl. Algebra, 195(3) (2005), 231-242.
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  • Acta Math. Sin. (Engl. Ser.), 22(4) (2006), 989-998.
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  • 525-537.
  • [11] M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser.
  • A Math. Sci., 73(1) (1997), 14-17.
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  • Math. Sem. Univ. Hamburg, 61 (1991), 15-33.
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  • Algebra, 79(3) (1992), 293-312.
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  • Proc. Amer. Math. Soc., 57(2) (1976), 213-216.
Year 2017, , 1 - 22, 17.01.2017
https://doi.org/10.24330/ieja.295657

Abstract

References

  • [5] E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta
  • Math. Hungar., 107(3) (2005), 207-224.
  • [6] C. Y. Hong, N. K. Kim, T. K. Kwak and Y. Lee, Extensions of zip rings, J.
  • Pure Appl. Algebra, 195(3) (2005), 231-242.
  • [7] Z. K. Liu, Triangular matrix representations of rings of generalized power series,
  • Acta Math. Sin. (Engl. Ser.), 22(4) (2006), 989-998.
  • [8] G. Marks, On 2-primal Ore extensions, Comm. Algebra, 29(5) (2001), 2113-
  • 2123.
  • [9] R. Mazurek and M. Ziembowski, Uniserial rings of skew generalized power
  • series, J. Algebra, 318(2) (2007), 737-764
  • [10] L. Ouyang, Ore extensions of weak zip rings, Glasg. Math. J., 51(3) (2009),
  • 525-537.
  • [11] M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser.
  • A Math. Sci., 73(1) (1997), 14-17.
  • [12] P. Ribenboim, Rings of generalized power series: Nilpotent elements, Abh.
  • Math. Sem. Univ. Hamburg, 61 (1991), 15-33.
  • [13] P. Ribenboim, Noetherian rings of generalized power series, J. Pure Appl.
  • Algebra, 79(3) (1992), 293-312.
  • [14] J. M. Zelmanowitz, The finite intersection property on annihilator right ideals,
  • Proc. Amer. Math. Soc., 57(2) (1976), 213-216.
There are 20 citations in total.

Details

Journal Section Articles
Authors

Ouyang Lunqun This is me

Zhou Qiong This is me

Wu Jinfang This is me

Publication Date January 17, 2017
Published in Issue Year 2017

Cite

APA Lunqun, O., Qiong, Z., & Jinfang, W. (2017). EXTENSIONS OF Σ-ZIP RINGS. International Electronic Journal of Algebra, 21(21), 1-22. https://doi.org/10.24330/ieja.295657
AMA Lunqun O, Qiong Z, Jinfang W. EXTENSIONS OF Σ-ZIP RINGS. IEJA. January 2017;21(21):1-22. doi:10.24330/ieja.295657
Chicago Lunqun, Ouyang, Zhou Qiong, and Wu Jinfang. “EXTENSIONS OF Σ-ZIP RINGS”. International Electronic Journal of Algebra 21, no. 21 (January 2017): 1-22. https://doi.org/10.24330/ieja.295657.
EndNote Lunqun O, Qiong Z, Jinfang W (January 1, 2017) EXTENSIONS OF Σ-ZIP RINGS. International Electronic Journal of Algebra 21 21 1–22.
IEEE O. Lunqun, Z. Qiong, and W. Jinfang, “EXTENSIONS OF Σ-ZIP RINGS”, IEJA, vol. 21, no. 21, pp. 1–22, 2017, doi: 10.24330/ieja.295657.
ISNAD Lunqun, Ouyang et al. “EXTENSIONS OF Σ-ZIP RINGS”. International Electronic Journal of Algebra 21/21 (January 2017), 1-22. https://doi.org/10.24330/ieja.295657.
JAMA Lunqun O, Qiong Z, Jinfang W. EXTENSIONS OF Σ-ZIP RINGS. IEJA. 2017;21:1–22.
MLA Lunqun, Ouyang et al. “EXTENSIONS OF Σ-ZIP RINGS”. International Electronic Journal of Algebra, vol. 21, no. 21, 2017, pp. 1-22, doi:10.24330/ieja.295657.
Vancouver Lunqun O, Qiong Z, Jinfang W. EXTENSIONS OF Σ-ZIP RINGS. IEJA. 2017;21(21):1-22.