Karpuz, Eylem GuzelCevik, Ahmet SinanKoppitz, JoergCangul, Ismail Naci2020-03-262020-03-2620131687-1812https://dx.doi.org/10.1186/1687-1812-2013-78https://hdl.handle.net/20.500.12395/29828In 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 pi-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.en10.1186/1687-1812-2013-78info:eu-repo/semantics/openAccessBruck-Reilly extensiongeneralized Bruck-Reilly *-extensionpi-inverse monoidregular monoidArticleQ2WOS:000326449800001Q1