Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On graded nil good rings   In this paper we introduce and study the notion of a graded nil-good ring
which is graded by a group. We investigate extensions of graded nil-good rings
to graded group rings, Further, we discuss graded matrix ring extensions and
trivial extensions of graded nil-good rings. Furthermore, we show that the
class of graded rings which are nil-good and the class of graded nil-good rings
are not comparable. Moreover, we discuss the question of when the nil-good
property of the component, which corresponds to the identity element the
grading group, implies that the whole graded ring is graded nil-good is also
treated.

25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph