TY  - JOUR
TI  - Quasi-idempotent ranks of the proper ideals in finite symmetric inverse
semigroups
AB  - Let In and Sn be the symmetric inverse semigroup and the symmetric group on a finite chain Xn =
{1, . . . , n}, respectively. Also, let In,r = {α ∈ In : |im(α)| ≤ r} for 1 ≤ r ≤ n − 1. For any α ∈ In , if α ̸= α
2 = α
4
then
α is called a quasi-idempotent. In this paper, we show that the quasi-idempotent rank of In,r (both as a semigroup and
as an inverse semigroup) is (n
2
)
if r = 2, and (n
r
)
+ 1 if r ≥ 3. The quasi-idempotent rank of In,1 is n (as a semigroup)
and n − 1 (as an inverse semigroup).
AU  - BUGAY, Leyla
DO  - 10.3906/mat-2001-3
PY  - 2021
JO  - Turkish Journal of Mathematics
VL  - 45
IS  - 1
SN  - 1300-0098
SP  - 281
EP  - 287
DB  - TRDizin
UR  - http://search/yayin/detay/531618
ER  -