2014/02/13 by Omar A. Al-Mallah, Al-mallah, Omar
Mathematics · #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1402.3326
openalex publication_date 2014/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A ring A is called presimplifiable if whenever a; b belongs to A and a = ab, then either a = 0 or b is a unit in A. Let A be a commutative ring and G be an abelian torsion group. For the group ring A[G], we prove that A[G] is presimplifiable if and only if A is presimplifiable and G is a p-group with p belongs to the Jacobson radical of A, and it is shown that A[G] is domainlike (i.e all zero divisors are nilpotents) if and only if A is domainlike and G is a p-group and p is a nilpotent in A. Furthermore, whenever the group ring A[G] is presimplifiable we prove that A[H] is presimplifiable for any subgroup H of G. Also, for a torsion free group G we prove that A[G] is domainlike if and only if A[G] is integral domain.