Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unit-regular elements in restrictive semigroups of transformations and
  linear operators   Let $T(X)$ be the full transformation semigroup on a set $X$ and let $L(V)$
be the semigroup under composition of all linear operators on a vector space
$V$ over a field. For a nonempty subset $Y$ of $X$ and a subspace $W$ of $V$,
we consider the restrictive semigroups $\overline{T}(X, Y) = \{f\in T(X)\mid Yf
\subseteq Y\}$ and $\overline{L}(V, W) = \{f\in L(V)\mid Wf \subseteq W\}$
under composition. We characterize unit-regular elements in $\overline{T}(X,
Y)$ and $\overline{L}(V, W)$. Utilizing these, we characterize unit-regularity
of $\overline{T}(X, Y)$ and $\overline{L}(V, W)$. We prove that $f\in L(V)$ is
unit-regular if and only if nullity$(f) = {\rm corank}(f)$. A transformation
semigroup is called semi-balanced if all its elements are semi-balanced. We
determine a necessary and sufficient condition for $\overline{T}(X, Y)$ and
$L(V)$ to be semi-balanced.

14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg