On the \(le\)-semigroups whose semigroup of bi-ideal elements is a normal band

• Date: 2016
• Main Authors: Bhuniya, A. K., Kumbhakar, M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2016
• Subjects: bi-ideal elements; duo; intra-regular; lattice-ordered semigroup; locally testable; normal band; regular; 06F05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/141
• Journal Title: Algebra and Discrete Mathematics

It is well known that the semigroup \(\mathcal{B}(S)\) of all bi-ideal elements of an \(le\)-semigroup \(S\) is a band if and only if \(S\) is both regular and intra-regular. Here we show that \(\mathcal{B}(S)\) is a band if and only if it is a normal band and give a complete characterization of the...