Geodesic
On the set of (b, c)-invertible elements
Filomat, Tome 37 (2023) no. 9, p. 2743

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

Let b and c be two elements in a semigroup S. This paper is devoted to studying the structures of S ||(b,c) and H (b,c) in a semigroup S, where S ||(b,c) stands for the set of all (b, c)-invertible elements and H (b,c) = {y ∈ S | bS 1 = yS 1 , S 1 y = S 1 c}. Denote the (b, c)-inverse of a ∈ S ||(b,c) by a ||(b,c). If S ||(b,c) ∅, then H (b,c) = {a ||(b,c) | a ∈ S ||(b,c) }. We first find some new equivalent conditions for H (b,c) to be a group and analyze its structure from the viewpoint of generalized inverses. Then a necessary and sufficient condition under which S ||(b,c) is a subsemigroup of S with the reverse order law holding for (b, c)-inverses is presented. At last, given a, b, c, d, x, y, z ∈ S and y ∈ S ||(b,c) , we prove that any two of the conditions x ∈ S ||(a,c) , z ∈ S ||(b,d) and zy ||(b,c) x ∈ S ||(a,d) imply the rest one.
DOI : 10.2298/FIL2309743S
Classification : 15A09, 20M10
Keywords: (b, c)-inverse, Green’s relations, reverse order law, semigroup 
Guiqi Shi; Jianlong Chen. On the set of (b, c)-invertible elements. Filomat, Tome 37 (2023) no. 9, p. 2743 . doi: 10.2298/FIL2309743S
@article{10_2298_FIL2309743S,
     author = {Guiqi Shi and Jianlong Chen},
     title = {On the set of (b, c)-invertible elements},
     journal = {Filomat},
     pages = {2743 },
     year = {2023},
     volume = {37},
     number = {9},
     doi = {10.2298/FIL2309743S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2309743S/}
}
TY  - JOUR
AU  - Guiqi Shi
AU  - Jianlong Chen
TI  - On the set of (b, c)-invertible elements
JO  - Filomat
PY  - 2023
SP  - 2743 
VL  - 37
IS  - 9
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2309743S/
DO  - 10.2298/FIL2309743S
LA  - en
ID  - 10_2298_FIL2309743S
ER  - 
%0 Journal Article
%A Guiqi Shi
%A Jianlong Chen
%T On the set of (b, c)-invertible elements
%J Filomat
%D 2023
%P 2743 
%V 37
%N 9
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2309743S/
%R 10.2298/FIL2309743S
%G en
%F 10_2298_FIL2309743S

Cité par Sources :