Let $S$ be a (multiplicatively written) semigroup $S$. Equipped with the (binary) operation of setwise multiplication $(X, Y) \mapsto \{xy \colon x \in X, \, y \in Y\}$, the family of all non-empty subsets of $S$ is then itself a (multiplicatively written) semigroup, herein denoted by $\mathcal P(S)$ and called the power semigroup of $S$.

To the best of my knowledge, power semigroups were first explicitly studied by Tamura and Shafer in the late 1960s. In particular, the earliest reference I've been able to track down is

T. Tamura and J. Shafer, On power semigroups, Math. Jap. 12 (1967), 25-32

Unfortunately, I don't have a copy of the paper and my understanding of its content is limited to a zbMATH review by McAlister. In any case, a question arised (I believe) from Tamura and Shafer's work was to prove (or disprove) that $\mathcal P(S)$ is (semigroup-)isomorphic to the power semigroup $\mathcal P(T)$ of a semigroup $T$ (if and) only if $S$ is isomorphic to $T$. The question was answered (in the negative) by E. M. Mogiljanskaja, see

Non-isomorphic semigroups with isomorphic semigroups of subsets, Semigroup Forum 6 (1973), 330-333

and references therein. But Mogiljanskaja writes,

The problem was proposed by: B. M. Schein (1960), T. Tamura (1967) [5] and others.

Here, [5] is

T. Tamura, Unsolved problems on semigroups, Sem. Reports. of Math. Sci., (1967), 33-35.

Unfortunately, I don't have a copy of this last paper either. So, I'm writing to ask if anybody can provide additional details and shed light on (some of) the unclear aspects of this story. In particular, I've the following questions:

Q1. Is it really that power semigroups were first explicitly considered by Tamura and Shafer? I've tried to look up the keywords "power" and "global" in Howie's and Clifford & Preston's monographs on semigroups, but haven't come up with anything (some people refer to power semigroups as globals). Q2. Which work of Schein is Mogiljanskaja referring to in the excerpt from their 1973 paper that I quoted in the above? This may be relevant to Q1, as Mogiljanskaja's words seem to suggest that Schein (I suppose this is Boris Moiseyevich Schein) had already considered power semigroups as early as 1960.