Abstract
In this paper, we determine necessary and sufficient conditions for Bruck-Reilly and generalized Bruck-Reilly ∗-extensions of arbitrary monoids to be
regular, coregular
and
strongly
π
-
inverse
. These
semigroup classes
have applications in various field of mathematics, such as matrix theory, discrete mathematics and
p
-adic analysis (especially in operator theory). In addition, while regularity and coregularity have so many applications in the meaning of boundaries (again in operator theory), inverse monoids and Bruck-Reilly extensions contain a mixture fixed-point results of algebra, topology and geometry within the purposes of this journal.
MSC:
20E22, 20M15, 20M18.