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http://dx.doi.org/10.4134/JKMS.2009.46.2.295

THE GROUP OF UNITS OF SOME FINITE LOCAL RINGS I  

Woo, Sung-Sik (DEPARTMENT OF MATHEMATICS EWHA WOMEN'S UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.2, 2009 , pp. 295-311 More about this Journal
Abstract
The purpose of this paper is to identify the group of units of finite local rings of the types ${\mathbb{F}}_2[X]/(X^k)$ and ${\mathbb{Z}}_4[X]/I$, 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;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
Times Cited By Web Of Science : 2  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
연도 인용수 순위
1 S. S. Woo, Cyclic codes of even length over $Z_4$, J. Korean Math. 44 (2007), no. 3, 697–706.   과학기술학회마을   DOI   ScienceOn
2 S. S. Woo, The group of units of some finite local rings II, J. Korean Math. 46 (2009), no. 3, 475–491.   과학기술학회마을   DOI   ScienceOn
3 S. S. Woo, The group of units of some finite local rings III, J. Korean Math. 46 (2009), no. 4, 675–689.   과학기술학회마을   DOI   ScienceOn
4 B. R. McDonald, Finite Rings with Identity, Pure and Applied Mathematics, Vol. 28. Marcel Dekker, Inc., New York, 1974.
5 S. S. Woo, Algebras with a nilpotent generator over $\mathbb{Z}_{p{^2}}$ , Bull. Korean Math. Soc. 43 (2006), no. 3, 487–497.   과학기술학회마을   DOI   ScienceOn