Indrani Dutta     (Jadavpur University, 188, Raja S. C. Mallick Road, Kolkata – 700032, India)
Sukhendu Kar     (Jadavpur University, 188, Raja S. C. Mallick Road, Kolkata – 700032, India)


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 \(a,b,c,d,e\in S\). 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 \(P(S)\)?" 
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 \(S_1\) and \(S_2\) of \(K\), \(P(S_1)\cong P(S_2)\) implies that \(S_1\cong S_2\). So it is interesting to find the class of ternary semigroups which are globally determined. Here we will study the global determinism of ternary \(\ast\)-band.


Rectangular ternary band, Involution ternary semigroup, Involution ternary band, Ternary \(\ast\)-band, Ternary projection.

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DOI: http://dx.doi.org/10.15826/umj.2023.1.005

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