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Research Articles

Nicely-contractible ideals, z0−ideals and z−ideals in formal series rings in finitely many variables

Pages 1850-1865 | Received 28 Mar 2022, Accepted 27 Oct 2022, Published online: 21 Nov 2022

References

  • Aliabad, A. R., Mohamadian, R. (2013). On z− ideals and z0− ideals of power series rings. J. Math. Extensions. 7(2):93–108.
  • Anderson, D. D. (1994). A note on minimal prime ideals. Proc. AMS 122(1):13–14.
  • Arnold, J. T. (1973). Krull dimension in power series rings. Trans. AMS 177:299–304. DOI: 10.1090/S0002-9947-1973-0316451-8.
  • Arnold, J. T. (1973). Power series rings over Prufer domains. Pacific J. Math. 44:1–11. DOI: 10.2140/pjm.1973.44.1.
  • Arnold, J. T., Gilmer, R., Heinzer, W. (1977). Some countability conditions in a commutative ring. Ill. J. Math. 21:648–665.
  • Condo, J. T., Coykendall, J., Dobbs, D. E. (1996). Formal power series rings over zero-SFT-rings. Commun. Algebra 24(8):2687–2698. DOI: 10.1080/00927879608542649.
  • Fields, D. E. (1971). Zero divisors and nilpotent elements in power series rings. Proc. AMS 27(3):427–433.
  • Gilmer, R., Heinzer, W. (1980). The Laskerian property, power series rings and Noetherian spectra. Proc. AMS 79(1):13–16.
  • Hizem, S., Benhissi, A. (2011). Nonnil-Noetherian rings and the SFT-property. Rocky Mountain J. Math. 41(5):1483–1500.
  • Kang, B. G., Loper, K. A., Lucas, T. G., Park, M. H., Toan, P. T. (2013). The Krull dimension of power series rings over non-SFT-rings. J. Pure Appl. Algebra 217:254–258. DOI: 10.1016/j.jpaa.2012.06.006.
  • Roitman, M. (2015). Arnold’s theorem on the strongly finite type (SFT) property and the dimension of power series ring. Commun. Algebra 43:337–344. DOI: 10.1080/00927872.2014.897590.

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