#### Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups

Yıl: 2021 Cilt: 45 Sayı: 1 Sayfa Aralığı: 281 - 287 Metin Dili: İngilizce İndeks Tarihi: 06-07-2022

Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups

Öz:
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).
Anahtar Kelime:

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 APA BUGAY L (2021). Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups. , 281 - 287. 10.3906/mat-2001-3 Chicago BUGAY Leyla Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups. (2021): 281 - 287. 10.3906/mat-2001-3 MLA BUGAY Leyla Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups. , 2021, ss.281 - 287. 10.3906/mat-2001-3 AMA BUGAY L Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups. . 2021; 281 - 287. 10.3906/mat-2001-3 Vancouver BUGAY L Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups. . 2021; 281 - 287. 10.3906/mat-2001-3 IEEE BUGAY L "Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups." , ss.281 - 287, 2021. 10.3906/mat-2001-3 ISNAD BUGAY, Leyla. "Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups". (2021), 281-287. https://doi.org/10.3906/mat-2001-3
 APA BUGAY L (2021). Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups. Turkish Journal of Mathematics, 45(1), 281 - 287. 10.3906/mat-2001-3 Chicago BUGAY Leyla Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups. Turkish Journal of Mathematics 45, no.1 (2021): 281 - 287. 10.3906/mat-2001-3 MLA BUGAY Leyla Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups. Turkish Journal of Mathematics, vol.45, no.1, 2021, ss.281 - 287. 10.3906/mat-2001-3 AMA BUGAY L Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups. Turkish Journal of Mathematics. 2021; 45(1): 281 - 287. 10.3906/mat-2001-3 Vancouver BUGAY L Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups. Turkish Journal of Mathematics. 2021; 45(1): 281 - 287. 10.3906/mat-2001-3 IEEE BUGAY L "Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups." Turkish Journal of Mathematics, 45, ss.281 - 287, 2021. 10.3906/mat-2001-3 ISNAD BUGAY, Leyla. "Quasi-idempotent ranks of the proper ideals in finite symmetric inverse semigroups". Turkish Journal of Mathematics 45/1 (2021), 281-287. https://doi.org/10.3906/mat-2001-3