Green's relations and congruences for ?-semigroups [i.e. Gamma-semigroups]
Thesis (M.Sc., Mathematics and Statistics)--Prince of Songkla University, 2008
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Prince of Songkla University
2022
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| Online Access: | http://kb.psu.ac.th/psukb/handle/2016/17362 |
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th-psu.2016-173622022-01-04T09:13:30Z Green's relations and congruences for ?-semigroups [i.e. Gamma-semigroups] ความสัมพันธ์ของกรีนและสมภาคสำหรับแกมมากึ่งกรุป Prathana Siammai Ronnason Chinram Faculty of Science (Mathemetics and Statistics) คณะวิทยาศาสตร์ ภาควิชาคณิตศาสตร์และสถิติ Semigroup algebras Green's function Congruences (Mathematics) Thesis (M.Sc., Mathematics and Statistics)--Prince of Songkla University, 2008 Let S be a Γ-semigroup and α a fixed element in Γ. Define ab = aαb for all a, b ∈ S. Then S is a semigroup and we denote this semigroup by Sα. Green’s relations L, R, H and D on a Γ-semigroups S were defined by N. K. Saha in the year 1987. The L-class, R-class, H-class and D-class containing the element a of a Γ-semigroup S will be written as La, Ra, Ha and Da, respectively. We study Green’s relations for Γ-semigroups and give some interesting properties. For example, we prove that if a and b are elements in a Γ-semigroup S such that aDb, then |La| = |Lb|, |Ra| = |Rb| and |Ha| = |Hb|. We also observe that if a is an element in a Γ-semigroup S and α ∈ Γ, then HaαHa ∩ Ha = ∅ or HaαHa = Ha. Moreover, if HaαHa = Ha, then Ha is a subsemigroup of Sα. Furthermore, we study congruences for Γ-semigroups and give some connections between congruences and their quotient sets on Green’s relations. We also define two congruences ρr and ρl on a Γ-semigroup S as follows: ρr = {(a, b) ∈ S × S | aγt = bγt for all t ∈ S and γ ∈ Γ}; ρl = {(a, b) ∈ S × S | tγa = tγb for all t ∈ S and γ ∈ Γ}. If S is a regular Γ-semigroup, we obtain that ρr and ρl are the minimum right and left reductive congruences on S, respectively. 2022-01-04T09:12:57Z 2022-01-04T09:12:57Z 2008 Thesis http://kb.psu.ac.th/psukb/handle/2016/17362 en Attribution-NonCommercial-NoDerivs 3.0 Thailand http://creativecommons.org/licenses/by-nc-nd/3.0/th/ application/pdf Prince of Songkla University |
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Prince of Songkhla University |
| building |
Khunying Long Athakravi Sunthorn Learning Resources Center |
| continent |
Asia |
| country |
Thailand Thailand |
| content_provider |
Khunying Long Athakravi Sunthorn Learning Resources Center |
| collection |
PSU Knowledge Bank |
| language |
English |
| topic |
Semigroup algebras Green's function Congruences (Mathematics) |
| spellingShingle |
Semigroup algebras Green's function Congruences (Mathematics) Prathana Siammai Green's relations and congruences for ?-semigroups [i.e. Gamma-semigroups] |
| description |
Thesis (M.Sc., Mathematics and Statistics)--Prince of Songkla University, 2008 |
| author2 |
Ronnason Chinram |
| author_facet |
Ronnason Chinram Prathana Siammai |
| format |
Theses and Dissertations |
| author |
Prathana Siammai |
| author_sort |
Prathana Siammai |
| title |
Green's relations and congruences for ?-semigroups [i.e. Gamma-semigroups] |
| title_short |
Green's relations and congruences for ?-semigroups [i.e. Gamma-semigroups] |
| title_full |
Green's relations and congruences for ?-semigroups [i.e. Gamma-semigroups] |
| title_fullStr |
Green's relations and congruences for ?-semigroups [i.e. Gamma-semigroups] |
| title_full_unstemmed |
Green's relations and congruences for ?-semigroups [i.e. Gamma-semigroups] |
| title_sort |
green's relations and congruences for ?-semigroups [i.e. gamma-semigroups] |
| publisher |
Prince of Songkla University |
| publishDate |
2022 |
| url |
http://kb.psu.ac.th/psukb/handle/2016/17362 |
| _version_ |
1735499217868161024 |