Global determinism of ternary semilattices

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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“…Since {x} is not a maximal element of X, σ({x}) is also not a maximal element of σ(X). Then from [8], we can write…”

Section: P R O O Fmentioning

confidence: 99%

Ternary ∗-Bands Are Globally Determined

Dutta

Kar

2023

UMJ

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On some properties of hyperideals in ternary hypersemirings

Mandal

Tamang

Das

2022

Asian-European J. Math.

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In this paper, we introduce the notion of prime hyperideals and maximal hyperideals in ternary hypersemirings and we study some of their properties. We construct a ternary semiring [Formula: see text], corresponding to a strongly distributive ternary hypersemiring [Formula: see text] and obtain various results among them. We also establish an inclusion preserving bijection between the set of all prime hyperideals of [Formula: see text] and collection of all prime total k-ideals of [Formula: see text].

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Global determinism of ternary semilattices

Cited by 2 publications

References 11 publications

Ternary ∗-Bands Are Globally Determined

Ternary ∗-Bands Are Globally Determined

On some properties of hyperideals in ternary hypersemirings

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