Ch. Manikya Rao1,
P. Koteswara Rao2 and D. Madhusudhana Rao3
1 Department of Mathematics, Bapatla Arts &
Sciences College, Bapatla, Guntur
(Dt), A. P. India. Email : firstname.lastname@example.org
2Acharya Nagarjuna University, Nagarjuna Nagar,
1Department of Mathematics, V. S. R & N. V. R.
College, Tenali, A. P. India. Email : email@example.com
In this paper, the terms, ‘A-potent’, ‘left A-divisor’, ‘right
A-divisor’, ‘A-divisor’ elements, ‘N(A)-ternary semigroup’ for an ideal A of a ternary
semigroup are introduced. If A is an ideal of a ternary semigroup T then it is
(1) (2) N0(A) = A2, N1(A)
is a semiprime ideal of T containing A, N2(A) = A4 are
equivalent, where No(A) = The set of all A-potent elements in T, N1(A)
= The largest ideal contained in No(A), N2(A) = The union
of all A-potent ideals. If A is a
semipseudo symmetric ideal of a ternary semigroup then it is proved that N0(A)
= N1(A) = N2(A).
It is also proved that if A is an ideal of a ternary semigroup such that
N0(A) = A then A is a completely semiprime ideal. Further it is proved that if A is an ideal of
ternary semigroup T then R(A), the divisor radical of A, is the union of all A-divisor
ideals in T. In a N(A)- ternary semigroup
it is proved that R(A) = N1(A). If A is a semipseudo symmetric ideal
of a semigroup T then it is proved that S is an N(A)- ternary semigroup iff
R(A) = N0(A). It is also proved
that if M is a maximal ideal of a ternary semigroup T containing a pseudo
symmetric ideal A then M contains all A-potent elements in T or T\M is
singleton which is A-potent.
Mathematical subject classification (2010) : 20M07; 20M11; 20M12.
symmetric ideal, semipseudo symmetric ideal, prime ideal, semiprime ideal,
completely prime ideal, completely semiprime ideal, semisimple element,
A-potent element, A-potent ideal, A-divisor, N(A)- ternary semigroup.