Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group invertibility of the sum in rings and its applications   We present new additive results for the group invertibility in a ring. Then
we apply our results to block operator matrices over Banach spaces and derive
the existence of group inverses of $2\times 2$ block operator matrices. These
generalize many known results, e.g., Benitez, Liu and Zhu(Linear Multilinear
Algebra, {\bf 59}(2011), 279--289) and Zhou, Chen and Zhu(Comm. Algebra, {\bf
48}(2020),676-690).

37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg