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THE GROUP OF UNITS OF SOME FINITE LOCAL RINGS II

  • Woo, Sung-Sik
  • Published : 2009.05.01

Abstract

In [2], we identified the group of units of finite local rings $\mathbb{Z}_4[X]$/($X^k+2X^a$, $2X^r$) with certain restrictions on a. In this paper we find direct sum decomposition of the group of units of such rings without restrictions on a into cyclic subgroups by finding their generators. And further generalization is considered.

Keywords

finite local ring;group of units

References

  1. Bernard R. McDonald, Finite Rings with Identity, Pure and Applied Mathematics, Vol. 28. Marcel Dekker, Inc., New York, 1974
  2. S. S. Woo, The group of units of some finite local rings I, J. Korean Math. Soc. 46 (2009), no. 2, 295–311 https://doi.org/10.4134/JKMS.2009.46.2.295
  3. S. S. Woo, The group of units of some finite local rings III, J. Korean Math. Soc. 46 (2009), no. 4, 675–689 https://doi.org/10.4134/JKMS.2009.46.4.675

Cited by

  1. THE GROUP OF UNITS OF SOME FINITE LOCAL RINGS III vol.46, pp.4, 2009, https://doi.org/10.4134/JKMS.2009.46.4.675
  2. THE GROUP OF UNITS OF SOME FINITE LOCAL RINGS I vol.46, pp.2, 2009, https://doi.org/10.4134/JKMS.2009.46.2.295