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Research Article Open access CC BY 4.0

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 · pp. 137–154 · Published 16 Oct 2021

10.9734/jamcs/2021/v36i830396

Abstract

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 determine the structures of the unit groups of R for all its characteristics.

Completely primary finite rings five radical zero unit groups

References (7)

  1. 1 Finite associative rings
  2. 2 Unit groups of some classes of power four radical zero commutative completely primary finite rings [DOI]
  3. 3 Unit groups of cube radical zero commutative completely primary finite rings [DOI]
  4. 4 Rings with few zero divisors [DOI]
  5. 5 Finite rings in which the product of any two zero divisors is zero [DOI]
  6. 6 On Unit Groups of Completely Primary Finite Rings [DOI]
  7. 7 Finite rings in which the multiplication of any two zero-divisors is zero [DOI]

Cited by 5

Characterization of Group of Invertible Elements of Six Index Zero Completely Primary Finite Rings of Characteristic p

Hezron Were, Nicholas Waweru, Edward Njuguna · Wasit Journal for Pure sciences · 2025

Classification of Unit Groups of Five Radical Zero Completely Primary Finite Rings Whose First and Second Galois Ring Module Generators Are of the Order pk, k = 2, 3, 4

Hezron Saka Were, Maurice Owino Oduor · Journal of Mathematics · 2022

On the Structures of a Class of Finite Rings of Five Radical Zero Completely Primary of Characteristic p

Hezron Saka Were · Earthline Journal of Mathematical Sciences · 2026

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