Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On presimplifiable group rings   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.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom