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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| Main Authors: | , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77957235672&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/49249 |
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| Institution: | Chiang Mai University |
| Summary: | 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. |
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