Magnifying Elements in the Generalized Semigroups of Transformations Preserving an Equivalence Relation
Thesis (M.Sc., Mathematics)--Prince of Songkla University, 2020
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Prince of Songkla University
2021
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| Online Access: | http://kb.psu.ac.th/psukb/handle/2016/17164 |
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th-psu.2016-171642021-07-30T09:11:54Z Magnifying Elements in the Generalized Semigroups of Transformations Preserving an Equivalence Relation สมาชิกขยายในกึ่งกรุปการแปลงวางนัยทั่วไปคงสภาพความสัมพันธ์สมมูล Thananya Kaewnoi Ronnason Chinram Faculty of Science (Mathemetics and Statistics) คณะวิทยาศาสตร์ ภาควิชาคณิตศาสตร์และสถิติ Semigroups Thesis (M.Sc., Mathematics)--Prince of Songkla University, 2020 An element a of a semigroup S is called a left (right) magnifying element if there exists a proper subset M of S such that aM = S (Ma = S). Let T(X) and P(X) denote the semigroup of the full and partial transformations on a nonempty set X, respectively. For an equivalence relation E and a partition P = {X; | i E A} on the set X, let TE(X) = {a e T(X)(x,y) E E implies (xa, ya) € E}, PE(X) = {a e P(X)(x,y) € E implies (2a, ya) € E}, T(X,P) = {a ET(X) Xịa CX, for all i E A}, and P(X,P) = {a e P(X) Xịa CX; for all i E A} Then TE(X), PE(X), T(X, P) and P(X, P) are semigroups under the composition of functions, as well. The main purpose of this thesis is to provide the properties of magnifying elements in the semigroups TE(X), PE(X), TE(X,P) = TE(X) n T(X,P) and PE(X,P) = PE(X) n P(X,P). Futhermore, the necessary and sufficient conditions for elements in these semigroups to be a left or right magnifying element are established. 2021-07-24T06:29:14Z 2021-07-24T06:29:14Z 2020 Thesis http://kb.psu.ac.th/psukb/handle/2016/17164 en Attribution-NonCommercial-NoDerivs 3.0 Thailand http://creativecommons.org/licenses/by-nc-nd/3.0/th/ application/pdf Prince of Songkla University |
| institution |
Prince of Songkhla University |
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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 |
Semigroups |
| spellingShingle |
Semigroups Thananya Kaewnoi Magnifying Elements in the Generalized Semigroups of Transformations Preserving an Equivalence Relation |
| description |
Thesis (M.Sc., Mathematics)--Prince of Songkla University, 2020 |
| author2 |
Ronnason Chinram |
| author_facet |
Ronnason Chinram Thananya Kaewnoi |
| format |
Theses and Dissertations |
| author |
Thananya Kaewnoi |
| author_sort |
Thananya Kaewnoi |
| title |
Magnifying Elements in the Generalized Semigroups of Transformations Preserving an Equivalence Relation |
| title_short |
Magnifying Elements in the Generalized Semigroups of Transformations Preserving an Equivalence Relation |
| title_full |
Magnifying Elements in the Generalized Semigroups of Transformations Preserving an Equivalence Relation |
| title_fullStr |
Magnifying Elements in the Generalized Semigroups of Transformations Preserving an Equivalence Relation |
| title_full_unstemmed |
Magnifying Elements in the Generalized Semigroups of Transformations Preserving an Equivalence Relation |
| title_sort |
magnifying elements in the generalized semigroups of transformations preserving an equivalence relation |
| publisher |
Prince of Songkla University |
| publishDate |
2021 |
| url |
http://kb.psu.ac.th/psukb/handle/2016/17164 |
| _version_ |
1709756007536656384 |