Extensions of Soft Ideals over Semigroups
Essam Hamouda, A. A. Ramadan and S. Amira
Let (𝐹, 𝐴) be a soft ideal over a semigroup 𝑆. We introduce the concept of the extension of (𝐹, 𝐴). By using the mapping α𝐹 corresponding to (𝐹, 𝐴), we define the notions α−prime and α−semiprime soft sets over 𝑆. Relationships between these concepts are investigated and illustrative examples are provided. Also, by means of the extensions of a soft ideal (𝐹, 𝐴), a congruence relation η𝐹 on 𝑆 is defined. It is shown that η𝐹 is a semilattice congruence if (𝐹, 𝐴) is a α−semiprime soft left ideal over 𝑆. Finally, the soft sets (𝑖𝐹 , 𝐴) and (𝐼𝐹 , 𝐴) over 𝑆 are defined in terms of the concept of soft points.
Keywords: Soft semigroups, soft left (right) ideals, soft points, extensions of soft ideals