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Primary and semiprimary г-ideals In г -semigroups

D. Madhusudhana Rao1, A. Anjaneyulu2, A. Gangadhara Rao3.

Department of Mathematics, V S R & N V R College, Tenali, A.P. India. Email ID:  dmrmaths@gmail.com , anjaneyulu.addala@gmail.com , raoag1967@gmail.com

 

 

 

ABSTRACT                                                                 


                 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-1M is primary Γ -ideal of S, where M is the unique maximal Γ-ideal of S. Further it is proved that in quasi commutative Γ-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 Γ-semigroup, 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.

Key words: Left Primary Γ-ideal, right primary Γ-ideal, primary Γ-ideal, left primary Γ-semigroup, right primary Γ-semigroup and primary Γ-semigroup, semiprimary Γ-ideal.

 

 

 

 

 


International eJournal of Mathematical Sciences, Technology and Humanities

Volume 2, Issue 1, Pages:  282 - 293