PRIMARY AND SEMIPRIMARY г-IDEALS IN г -SEMIGROUPS
D. Madhusudhana Rao, A. S. R. Anjaneyulu, A. Gangadhara Rao · 2012
In this paper a Γ -semigroup S with identity, if √A = M for some Γ -ideal of S, where M is the unique maximal Γ-ideal of S, then A is a primary Γ -ideal. It is proved that if S is a Γ semigroup with identity, then for any natural number n, (MΓ) n-1 M is primary Γ -ideal of S, where M is the unique maximal Γ-ideal of S. Further it is proved that in quasi commutative semigroup S, a Γ-ideal A of S is left primary iff A is right primary. It is proved that in semipseudo symmetric semiprimary Γ-semigroup, globally idempotent principal Γ-ideals form a chain under set inclusion. In a semisimple Γ-semigroup S it is proved that the conditions every ideal of S is prime, S is a primary Γ-semigroup, S is a left primary Γsemigroup, S is a right primary Γ-semigroup, S is a semiprimary Γ-semigroup, prime Γ-ideals of S form a chain, principal Γ-ideals of S form a chain, Γ-ideals of S form a chain are equivalent. Mathematical subject classification (2010) : 20M07; 20M11; 20M12.