Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: W-core inverses in rings with involution   Let $R$ be a unital $*$-ring and let $a,w,v\in R$. The initial goal of this
work is to introduce two new classes of generalized inverses, called the
$w$-core inverse and the dual $v$-core inverse. It is shown that the core
inverse and the pseudo core inverse belongs to the defined $w$-core inverse,
and the dual core inverse and the dual pseudo core inverse are instances of the
dual $v$-core inverse. An element $a\in R$ is $w$-core invertible if there
exists some $x\in R$ such that $awx^2=x$, $xawa=a$ and $(awx)^*=awx$. Such an
$x$ is called a $w$-core inverse of $a$. The dual $v$-core inverse of $a$ is
defined by the existence of $y\in R$ satisfying $y^2va=y$, $avay=a$ and
$(yva)^*=yva$. Several characterizations of them are given, and the expression
of the $w$-core inverse (resp. the dual $v$-core inverse) of $a$ is given by
the inverse of $w$ along $a$ and $\{1,3\}$-inverses of $a$ (resp. the inverse
of $v$ along $a$ and $\{1,4\}$-inverses of $a$). Also, the characterization for
both $w$-core invertible and dual $v$-core invertible elements is given by
units. Finally, the relationships among the $w$-core inverse, the dual $v$-core
inverse and other generalized inverses are given.

22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas