Injective transformations with equal gap and defect
Suppose that X is an infinite set and I(X) is the symmetric inverse semigroup defined on X. If α ε I(X), we let dom α and ran α denote the domain and range of α , respectively, and we say that g(α)=|X/domα| and d(α)=|X/ranα| is the gap and the defect of , respectively. In this paper, we study algebr...
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th-cmuir.6653943832-597432018-09-10T03:20:51Z Injective transformations with equal gap and defect Jintana Sanwong R. P. Sullivan Mathematics Suppose that X is an infinite set and I(X) is the symmetric inverse semigroup defined on X. If α ε I(X), we let dom α and ran α denote the domain and range of α , respectively, and we say that g(α)=|X/domα| and d(α)=|X/ranα| is the gap and the defect of , respectively. In this paper, we study algebraic properties of the semigroup $A(X)=\{α I(X) g(α )=d(α). For example, we describe Greens relations and ideals in A(X), and determine all maximal subsemigroups of A(X) when X is uncountable. Copyright © Australian Mathematical Society 2009. 2018-09-10T03:20:51Z 2018-09-10T03:20:51Z 2009-04-01 Journal 17551633 00049727 2-s2.0-77957235672 10.1017/S0004972708001330 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77957235672&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/59743 |
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Mathematics Jintana Sanwong R. P. Sullivan Injective transformations with equal gap and defect |
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Suppose that X is an infinite set and I(X) is the symmetric inverse semigroup defined on X. If α ε I(X), we let dom α and ran α denote the domain and range of α , respectively, and we say that g(α)=|X/domα| and d(α)=|X/ranα| is the gap and the defect of , respectively. In this paper, we study algebraic properties of the semigroup $A(X)=\{α I(X) g(α )=d(α). For example, we describe Greens relations and ideals in A(X), and determine all maximal subsemigroups of A(X) when X is uncountable. Copyright © Australian Mathematical Society 2009. |
| format |
Journal |
| author |
Jintana Sanwong R. P. Sullivan |
| author_facet |
Jintana Sanwong R. P. Sullivan |
| author_sort |
Jintana Sanwong |
| title |
Injective transformations with equal gap and defect |
| title_short |
Injective transformations with equal gap and defect |
| title_full |
Injective transformations with equal gap and defect |
| title_fullStr |
Injective transformations with equal gap and defect |
| title_full_unstemmed |
Injective transformations with equal gap and defect |
| title_sort |
injective transformations with equal gap and defect |
| publishDate |
2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77957235672&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/59743 |
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