TERNARY *-BANDS ARE GLOBALLY DETERMINED

Abstract

A non-empty set S together with the ternary operation denoted by juxtaposition is said to be ternary semigroup if it satisfies the associativity property ab(cde)=a(bcd)e=(abc)de for all a,b,c,d,e∈S. The global set of a ternary semigroup S is the set of all non empty subsets of S and it is denoted by P(S). If S is a ternary semigroup then P(S) is also a ternary semigroup with a naturally defined ternary multiplication. A natural question arises: ``Do all properties of S remain the same in P(S)?'' %one may ask is that ``is all property of S remain same in P(S)?". The global determinism problem is a part of this question. A class K of ternary semigroups is said to be globally determined if for any two ternary semigroups S1 and S2 of K, P(S1)≅P(S2) implies that S1≅S2. So it is interesting to find the class of ternary semigroups which are globally determined. Here we will study the global determinism of ternary ∗-band.