@article{article_745821, title={Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n}, journal={Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi}, volume={22}, pages={669–678}, year={2020}, DOI={10.25092/baunfbed.745821}, url={https://izlik.org/JA35AC57RY}, author={Bugay, Leyla}, keywords={Simetrik inverse yarıgrup,quasi-idempotent,rank}, abstract={Let I_n, S_n and A_n be the symmetric inverse semigroup, the symmetric group and the alternating group on X_n={1,…,n}, for n≥2, respectively. Also let I_(n,r) be the subsemigroup consists of all partial injective maps with height less than or equal to r for 1≤r≤n-1, and let SI_(n,r)=I_(n,r)∪S_n and AI_(n,r)=I_(n,r)∪A_n. A non-idempotent element whose square is an idempotent is called a quasi-idempotent. In this paper we obtain the rank and the quasi-idempotent rank of SI_(n,r) (of AI_(n,r)). Also we obtain the relative rank and the relative quasi-idempotent rank of SI_(n,r) modulo S_n (of AI_(n,r) modulo A_n).}, number={2}