On the semigroup of injective transformations with restricted range that equal gap and defect

• Date: 2025
• Main Author: Singha, Boorapa
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2025
• Subjects: transformation semigroup; Green's relation; natural partial order; 20M20
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2335
• Journal Title: Algebra and Discrete Mathematics

Let \(X\) be an infinite set and \(I(X)\) the symmetric inverse semigroup on \(X\). Let \(A(X)=\{\alpha \in I(X):|X\setminus \mathrm{dom\;}\alpha|=|X\setminus X\alpha|\}\), it is known that \(A(X)\) is the largest factorizable subsemigroup of \(I(X)\). In this article, for any nonempty subset \(Y\)...