Prime double-framed soft bi-ideals of ordered semigroup

Document Type : Original Article


1 The University of Haripur, KPK, Pakistan

2 Faculty of Engineering, Arab Academy for Science and Technology and Maritime Transport (AASTMT), Aswan Branch, Egypt

3 Department of Mathematics and Statistics, The University of Haripur, Haripur, KP, Pakistan

4 Higher Institute of Engineering and Technology King Marriott, P.O. Box 3135, Egypt

5 Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan


The notions of a prime (strongly prime, semiprime, irreducible, and strongly irreducible) double-framed soft bi-ideals (briefly, prime, (strongly prime, semiprime, irreducible and strongly irreducible) DFS bi-ideals) in ordered semigroups are introduced and related properties are investigated. Several examples of these notions are provided. The relationship between prime and strongly prime, irreducible and strongly irreducible DFS bi-ideals are considered and  haracterizations of these concepts are established. The Characterizations of regular and intraregular ordered semigroups in terms of these notions are studied.