Please use this identifier to cite or link to this item:
|Title:||On the groups of units of finite commutative chain rings|
|Citation:||Hou, X.-D., Leung, K.H., Ma, S.L. (2003-01). On the groups of units of finite commutative chain rings. Finite Fields and their Applications 9 (1) : 20-38. ScholarBank@NUS Repository. https://doi.org/10.1016/S1071-5797(02)00003-5|
|Abstract:||A finite commutative chain ring is a finite commutative ring whose ideals form a chain. Let R be a finite commutative ring with maximal ideal M and characteristic pn such that R/M ≅ GF(pr) and pR = Me, ≤s, where s is the nilpotency of M. When (P - 1) ł e, the structure of the group of units R× of R has been determined; it only depends on the parameters p, n, r, e, s. In this paper, we give an algorithmic method which allows us to compute the structure of R× when (p - 1) e; such a structure not only depends on the parameters p, n, r, e, s, but also on the Eisenstein polynomial which defines R as an extension over the Galois ring GR(pn, r). In the case (p - 1) ł e, we strengthen the known result by listing a set of linearly independent generators for R×. In the case (p - 1) e but p ł e, we determine the structure of R× explicitly. © 2002 Elsevier Science (USA). All rights reserved.|
|Source Title:||Finite Fields and their Applications|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Oct 15, 2018
WEB OF SCIENCETM
checked on Oct 8, 2018
checked on Sep 21, 2018
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.