Unit Groups of Classes of Five Radical Zero Commutative Completely Primary Finite Rings
Hezron Saka Were *
Department of Mathematics, Egerton University, P.O.Box 536-20115, Egerton, Kenya.
Maurice Oduor Owino
Department of Mathematics and Computer Science, University of Kabianga, P.O.Box 2030-20200, Kericho, Kenya.
Moses Ndiritu Gichuki
Department of Mathematics, Egerton University, P.O.Box 536-20115, Egerton, Kenya.
*Author to whom correspondence should be addressed.
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.
Keywords: Completely primary finite rings, five radical zero, unit groups