Hezron Saka Were

Classication of Units of Five Radical Zero Completely Primary Finite Rings with Variant Orders of Second Galois Ring Module Generators

Hezron Saka Were, Maurice Owino Oduor & Moses Ndiritu Gichuki · Asian Research Journal of Mathematics · 2022

Let \(R\) be a commutative completely primary finite ring with a unique maximal ideal \(Z(R)\) such that \((Z(R))^{5}=(0) ;(Z(R))^{4} \neq(0)\). Then \(R / Z(R) \cong G F\left(p^{r}\right)\) is a finite field of order \(p^{r}\). Let \(R_{0}=G R\left(p^{k r}, p^{k}\right)\) be a G...

Open access Research Article 10.9734/arjom/2022/v18i630385

Unit Groups of Classes of Five Radical Zero Commutative Completely Primary Finite Rings

Hezron Saka Were, Maurice Oduor Owino & Moses Ndiritu Gichuki · Journal of Advances in Mathematics and Computer Science · 2021

In this paper, R is considered a completely primary finite ring and Z(R) is its subset of all zero divisors (including zero), forming a unique maximal ideal. We give a construction of R whose subset of zero divisors Z(R) satisfies the conditions (Z(R))5 = (0); (Z(R))4 ̸= (0) and...

Open access Research Article 10.9734/jamcs/2021/v36i830396