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Simetrik inverse yarıgrubun S_n veya A_n i içeren bazı ideallerinin rankları

Yıl 2020, Cilt 22, Sayı 2, 669 - 678, 10.04.2020
https://doi.org/10.25092/baunfbed.745821

Öz

n≥2 için I_n, S_n ve A_n, sırasıyla, X_n={1,…,n} üzerindeki simetrik inverse yarıgrup, simetrik grup ve alterne grup olsun. Ayrıca, 1≤r≤n-1 için I_(n,r), yüksekliği en fazla r olan tüm kısmi bire-bir dönüşümlerden oluşan altyarıgrup, SI_(n,r)=I_(n,r)∪S_n ve AI_(n,r)=I_(n,r)∪A_n olsun. Karesi idempotent olan fakat kendisi idempotent olmayan bir elemana quasi-idempotent denir. Bu calışmada SI_(n,r) (AI_(n,r)) nin rankını elde ettik. Ayrıca, modulo S_n e göre SI_(n,r) nin (modulo A_n e göre AI_(n,r) nin) ilişkili rankını ve quasi-ilişkili rankını elde ettik.

Kaynakça

  • Ayık, G., Ayık, H., Howie, J. M., On factorisations and generators in transformation semigroup, Semigroup Forum, 70, 225–237, (2005). Ayık, G., Ayık, H., Howie, J. M., Ünlü, Y., Rank properties of the semigroup of singular transformations on a finite set, Communications in Algebra, 36, 2581–2587, (2008). Bugay L. Quasi-idempotent ranks of some permutation groups and transformation semigroups, Turkish Journal of Mathematics 43, 2390–2395, (2019). Ganyushkin, O., Mazorchuk, V., Classical Finite Transformation Semigroups, London, Springer-Verlag, (2009). Garba, G.U., On the idempotent ranks of certain semigroups of order-preserving transformations, Portugaliae Mathematica, 51, 185–204, (1994). Garba, G. U., Imam, A. T., Products of quasi-idempotents in finite symmetric inverse semigroups, Semigroup Forum, 92, 645–658, (2016). Howie, J. M., Fundamentals of Semigroup Theory. New York, Oxford University Press, (1995). Levi, I., McFadden, R. B., S_n-Normal semigroups, Proceedings of the Edinburgh Mathematical Society, 37, 471–476, (1994). Yiğit, E., Ayık, G., Ayık, H., Minimal relative generating sets of some partial transformation semigroups, Communications in Algebra, 45, 1239–1245, (2017). Zhao, P., Fernandes, V. H., The ranks of ideals in various transformation monoids, Communications in Algebra, 43, 674-692, (2015).

Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n

Yıl 2020, Cilt 22, Sayı 2, 669 - 678, 10.04.2020
https://doi.org/10.25092/baunfbed.745821

Öz

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).

Kaynakça

  • Ayık, G., Ayık, H., Howie, J. M., On factorisations and generators in transformation semigroup, Semigroup Forum, 70, 225–237, (2005). Ayık, G., Ayık, H., Howie, J. M., Ünlü, Y., Rank properties of the semigroup of singular transformations on a finite set, Communications in Algebra, 36, 2581–2587, (2008). Bugay L. Quasi-idempotent ranks of some permutation groups and transformation semigroups, Turkish Journal of Mathematics 43, 2390–2395, (2019). Ganyushkin, O., Mazorchuk, V., Classical Finite Transformation Semigroups, London, Springer-Verlag, (2009). Garba, G.U., On the idempotent ranks of certain semigroups of order-preserving transformations, Portugaliae Mathematica, 51, 185–204, (1994). Garba, G. U., Imam, A. T., Products of quasi-idempotents in finite symmetric inverse semigroups, Semigroup Forum, 92, 645–658, (2016). Howie, J. M., Fundamentals of Semigroup Theory. New York, Oxford University Press, (1995). Levi, I., McFadden, R. B., S_n-Normal semigroups, Proceedings of the Edinburgh Mathematical Society, 37, 471–476, (1994). Yiğit, E., Ayık, G., Ayık, H., Minimal relative generating sets of some partial transformation semigroups, Communications in Algebra, 45, 1239–1245, (2017). Zhao, P., Fernandes, V. H., The ranks of ideals in various transformation monoids, Communications in Algebra, 43, 674-692, (2015).

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Bilimler
Bölüm Araştırma Makalesi
Yazarlar

Leyla BUGAY Bu kişi benim (Sorumlu Yazar)
ÇUKUROVA ÜNİVERSİTESİ
0000-0002-8316-2763
Türkiye

Yayımlanma Tarihi 10 Nisan 2020
Başvuru Tarihi 3 Şubat 2020
Kabul Tarihi 14 Mayıs 2020
Yayınlandığı Sayı Yıl 2020, Cilt 22, Sayı 2

Kaynak Göster

Bibtex @araştırma makalesi { baunfbed745821, journal = {Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi}, issn = {1301-7985}, eissn = {2536-5142}, address = {Balıkesir Üniversitesi Rektörlük Binası 4.Kat Fen Bilimleri Enstitüsü Çağış / 10145-Balıkesir}, publisher = {Balıkesir Üniversitesi}, year = {2020}, volume = {22}, pages = {669 - 678}, doi = {10.25092/baunfbed.745821}, title = {Certain ranks of some ideals in symmetric inverse semigroups contains S\_n or A\_n}, key = {cite}, author = {Bugay, Leyla} }
APA Bugay, L. (2020). Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n . Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi , 22 (2) , 669-678 . DOI: 10.25092/baunfbed.745821
MLA Bugay, L. "Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n" . Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (2020 ): 669-678 <https://dergipark.org.tr/tr/pub/baunfbed/issue/53255/745821>
Chicago Bugay, L. "Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n". Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (2020 ): 669-678
RIS TY - JOUR T1 - Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n AU - Leyla Bugay Y1 - 2020 PY - 2020 N1 - doi: 10.25092/baunfbed.745821 DO - 10.25092/baunfbed.745821 T2 - Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi JF - Journal JO - JOR SP - 669 EP - 678 VL - 22 IS - 2 SN - 1301-7985-2536-5142 M3 - doi: 10.25092/baunfbed.745821 UR - https://doi.org/10.25092/baunfbed.745821 Y2 - 2020 ER -
EndNote %0 Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n %A Leyla Bugay %T Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n %D 2020 %J Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi %P 1301-7985-2536-5142 %V 22 %N 2 %R doi: 10.25092/baunfbed.745821 %U 10.25092/baunfbed.745821
ISNAD Bugay, Leyla . "Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n". Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 / 2 (Nisan 2020): 669-678 . https://doi.org/10.25092/baunfbed.745821
AMA Bugay L. Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n. BAUN Fen. Bil. Enst. Dergisi. 2020; 22(2): 669-678.
Vancouver Bugay L. Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2020; 22(2): 669-678.
IEEE L. Bugay , "Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n", Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 22, sayı. 2, ss. 669-678, Nis. 2020, doi:10.25092/baunfbed.745821