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Soft intersection semigroups, ideals and bi-ideals; A new application on semigroup theory I

Sezer Aslıhan Sezgin (Amasya University, Department of Mathematics, Amasya, Turkey)
Çağman Naim (Gaziosmanpaşa University, Department of Mathematics, Tokat, Turkey)
Atagü Akın Osman (Bozok University, Department of Mathematics, Yozgat, Turkey)
Irfan Ali Muhammed (COMSATS Institute of Information Technology Attock, Department of Mathematics, Attock, Pakistan)
Türkmen Ergül (Amasya University, Department of Mathematics, Amasya, Turkey)

In this paper, we define soft intersection semigroups, soft intersection left (right, two-sided) ideals and bi-ideals of semigroups, give their properties and interrelations and we characterize regular, intra-regular, completely regular, weakly regular and quasi-regular semigroups in terms of these ideals.

Keywords: soft set, Soft intersection left (right, two-sided) ideal, soft intersection bi-ideal, soft semiprime, regular semigroups