Global determinism of semigroups having regular globals

Gan, Aiping; Zhao, Xianzhong; Ren, Miaomiao

doi:10.1007/s10998-015-0107-y

Cited by 4 publications

(1 citation statement)

References 10 publications

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“…In 2014, A. Gan, X. Zhao and Y. Shao [1] proved that clifford semigroups are globally determined. In 2015, A. Gan, X. Zhao and M. Ren [3] studied the global determinism of semigroups having regular globals. A. Gan, X. Zhao and Y. Shao [2] also discussed the globals of idempotent semigroups in 2016 and in 2017, B. Yu, X. Zhao, A. Gan [12] proved that idempotent semigroups are globally determined.…”

Section: Introductionmentioning

confidence: 99%

Ternary ∗-Bands Are Globally Determined

Dutta

Kar

2023

UMJ

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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.

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