dc.contributor.author |
Were, Hezron Saka |
|
dc.contributor.author |
Oduor, Maurice Owino |
|
dc.contributor.author |
Gichuki, Ndiritu |
|
dc.date.accessioned |
2022-09-12T07:51:49Z |
|
dc.date.available |
2022-09-12T07:51:49Z |
|
dc.date.issued |
2022 |
|
dc.identifier.citation |
Were, H. S., Oduor, M. O., & Gichuki, M. N. Classification of Units of Five Radical Zero Completely Primary Finite Rings with Variant Orders of Second Galois Ring Module Generators. |
en_US |
dc.identifier.issn |
2456-477X |
|
dc.identifier.uri |
http://ir-library.kabianga.ac.ke/handle/123456789/408 |
|
dc.description |
Article Paper on Classification of Units of Five Radical Zero Completely
Primary Finite Rings with Variant Orders of Second
Galois Ring Module Generators |
en_US |
dc.description.abstract |
Let R be a commutative completely primary finite ring with a unique maximal ideal Z(R) such
that (Z(R))5 = (0); (Z(R))4
̸= (0). Then R/Z(R) ∼= GF(p
r
) is a finite field of order p
r
. Let
R0 = GR(p
kr, pk
) be a Galois ring of order p
kr and of characteristic p
k
for some prime number
p and positive integers k, r so that R = R0
⊕U
⊕V
⊕W
⊕Y , where U, V, W and Y are
R0/pR0 - spaces considered as R0 modules generated by e, f, g and h elements respectively.
Then R is of characteristic p
k where 1 ≤ k ≤ 5 . In this paper, we investigate and determine the
structures of the unit groups of some classes of commutative completely primary finite ring R
with pui = p
ξ
vj = pwk = pyl = 0, where ξ = 2, 3; 1 ≤ i ≤ e, 1 ≤ j ≤ f, 1 ≤ k ≤ g, and 1 ≤ l ≤ h. |
en_US |
dc.language.iso |
en |
en_US |
dc.publisher |
Asian Research Journal of Mathematics |
en_US |
dc.subject |
Completely primary finite ring |
en_US |
dc.subject |
Five radical zero |
en_US |
dc.subject |
Unit groups |
en_US |
dc.title |
Classification of Units of Five Radical Zero Completely Primary Finite Rings with Variant Orders of Second Galois Ring Module Generators |
en_US |
dc.type |
Article |
en_US |