Open Access Research

Some fixed-point results on (generalized) Bruck-Reilly ∗-extensions of monoids

Eylem Guzel Karpuz1*, Ahmet Sinan Çevik2, Jörg Koppitz3 and Ismail Naci Cangul4

Author Affiliations

1 Department of Mathematics, Kamil Özdag Science Faculty, Karamanoglu Mehmetbey University, Yunus Emre Campus, Karaman, 70100, Turkey

2 Department of Mathematics, Faculty of Science, Selçuk University, Campus, Konya, 42075, Turkey

3 Institute of Mathematics, Potsdam University, Potsdam, 14469, Germany

4 Department of Mathematics, Faculty of Arts and Science, Uludag University, Gorukle Campus, Bursa, 16059, Turkey

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Fixed Point Theory and Applications 2013, 2013:78  doi:10.1186/1687-1812-2013-78

Published: 29 March 2013

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 stronglyπ-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.

Keywords:
Bruck-Reilly extension; generalized Bruck-Reilly ∗-extension; π-inverse monoid; regular monoid