THE GROUP OF UNITS OF SOME FINITE LOCAL RINGS I

Title & Authors
THE GROUP OF UNITS OF SOME FINITE LOCAL RINGS I
Woo, Sung-Sik;

Abstract
The purpose of this paper is to identify the group of units of finite local rings of the types $\small{{\mathbb{F}}_2[X]/(X^k)}$ and $\small{{\mathbb{Z}}_4[X]/I}$, where I is an ideal. It turns out that they are 2-groups and we give explicit direct sum decomposition into cyclic subgroups of 2-power order and their generators.
Keywords
finite local ring;group of units;
Language
English
Cited by
1.
THE GROUP OF UNITS OF SOME FINITE LOCAL RINGS II,Woo, Sung-Sik;

대한수학회지, 2009. vol.46. 3, pp.475-491
2.
THE GROUP OF UNITS OF SOME FINITE LOCAL RINGS III,Woo, Sung-Sik;

대한수학회지, 2009. vol.46. 4, pp.675-689
References
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2.
S. S. Woo, Algebras with a nilpotent generator over \$\mathbb{Z}_{p{^2}}\$ , Bull. Korean Math. Soc. 43 (2006), no. 3, 487–497.

3.
S. S. Woo, Cyclic codes of even length over \$Z_4\$, J. Korean Math. 44 (2007), no. 3, 697–706.

4.
S. S. Woo, The group of units of some finite local rings II, J. Korean Math. 46 (2009), no. 3, 475–491.

5.
S. S. Woo, The group of units of some finite local rings III, J. Korean Math. 46 (2009), no. 4, 675–689.