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. Shafter, _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][1]. 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 (or Tamura and Shafer)? I've tried to look for 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 seems relevant to Q1, as it seems from Mogiljanskaja's words that Schein (I suppose this is Boris Moiseyevich Schein) had already considered power semigroups as early as 1960.

  [1]: https://zbmath.org/0189.30302