MVLSC Home โ€ข Issue Contents โ€ขย Forthcoming Papers

Extensions of Soft Ideals over Semigroups
Essam Hamouda, A. A. Ramadan and S. Amira

Let (๐น, ๐ด) be a soft ideal over a semigroup ๐‘†. We introduce the concept of the extension of (๐น, ๐ด). By using the mapping ฮฑ๐น corresponding to (๐น, ๐ด), we define the notions ฮฑโˆ’prime and ฮฑโˆ’semiprime soft sets over ๐‘†. Relationships between these concepts are investigated and illustrative examples are provided. Also, by means of the extensions of a soft ideal (๐น, ๐ด), a congruence relation ฮท๐น on ๐‘† is defined. It is shown that ฮท๐น is a semilattice congruence if (๐น, ๐ด) is a ฮฑโˆ’semiprime soft left ideal over ๐‘†. Finally, the soft sets (๐‘–๐น , ๐ด) and (๐ผ๐น , ๐ด) over ๐‘† are defined in terms of the concept of soft points.

Keywords: Soft semigroups, soft left (right) ideals, soft points, extensions of soft ideals

Full Text (IP)