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EXTENSIONS OF Σ-ZIP RINGS

Year 2017, Volume 21, Issue 21, 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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Year 2017, Volume 21, Issue 21, 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.

Details

Journal Section Articles
Authors

Ouyang LUNQUN This is me


Zhou QİONG This is me


Wu JİNFANG This is me

Publication Date January 17, 2017
Published in Issue Year 2017, Volume 21, Issue 21

Cite

Bibtex @research article { ieja295657, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2017}, volume = {21}, number = {21}, pages = {1 - 22}, doi = {10.24330/ieja.295657}, title = {EXTENSIONS OF Σ-ZIP RINGS}, key = {cite}, author = {Lunqun, Ouyang and Qiong, Zhou and Jinfang, Wu} }
APA Lunqun, O. , Qiong, Z. & Jinfang, W. (2017). EXTENSIONS OF Σ-ZIP RINGS . International Electronic Journal of Algebra , 21 (21) , 1-22 . DOI: 10.24330/ieja.295657
MLA Lunqun, O. , Qiong, Z. , Jinfang, W. "EXTENSIONS OF Σ-ZIP RINGS" . International Electronic Journal of Algebra 21 (2017 ): 1-22 <https://dergipark.org.tr/en/pub/ieja/issue/27921/295657>
Chicago Lunqun, O. , Qiong, Z. , Jinfang, W. "EXTENSIONS OF Σ-ZIP RINGS". International Electronic Journal of Algebra 21 (2017 ): 1-22
RIS TY - JOUR T1 - EXTENSIONS OF Σ-ZIP RINGS AU - OuyangLunqun, ZhouQiong, WuJinfang Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.295657 DO - 10.24330/ieja.295657 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 1 EP - 22 VL - 21 IS - 21 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.295657 UR - https://doi.org/10.24330/ieja.295657 Y2 - 2016 ER -
EndNote %0 International Electronic Journal of Algebra EXTENSIONS OF Σ-ZIP RINGS %A Ouyang Lunqun , Zhou Qiong , Wu Jinfang %T EXTENSIONS OF Σ-ZIP RINGS %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 21 %N 21 %R doi: 10.24330/ieja.295657 %U 10.24330/ieja.295657
ISNAD Lunqun, Ouyang , Qiong, Zhou , Jinfang, Wu . "EXTENSIONS OF Σ-ZIP RINGS". International Electronic Journal of Algebra 21 / 21 (January 2017): 1-22 . https://doi.org/10.24330/ieja.295657
AMA Lunqun O. , Qiong Z. , Jinfang W. EXTENSIONS OF Σ-ZIP RINGS. IEJA. 2017; 21(21): 1-22.
Vancouver Lunqun O. , Qiong Z. , Jinfang W. EXTENSIONS OF Σ-ZIP RINGS. International Electronic Journal of Algebra. 2017; 21(21): 1-22.
IEEE O. Lunqun , Z. Qiong and W. Jinfang , "EXTENSIONS OF Σ-ZIP RINGS", International Electronic Journal of Algebra, vol. 21, no. 21, pp. 1-22, Jan. 2017, doi:10.24330/ieja.295657