Power ternary semirings

In this paper, we introduce the notion of power ternary semiring as a generalization of power semirings introduced by Sen and Bhuniya (Semigr Forum 82:131–140, 2011). The main aim of this paper is twofold. The first one is to study some properties of power ternary semirings with the help of corresponding properties of ternary semigroups. The another important aspect is—if \(S_1\) and \(S_2\) are isomorphic ternary semigroups, then the corresponding power ternary semirings \(P(S_1)\) and \(P(S_2)\) are obviously isomorphic. It is quiet natural to ask whether the converse is true, i.e. is it true that for any ternary semigroups \(S_1\) and \(S_2\) it holds: \(P(S_1)\cong P(S_2)\) implies that \(S_1\cong S_2\)? In this paper, we try to answer this question partially.