Let $$\Lambda$$ be a class of Abelian groups. A group $$A\in\Lambda$$ is said to be determined by its endomorphism semigroup $$E^\star(A)$$ in the class $$\Lambda$$ if every isomorphism $$E^\star(A)\cong E^\star(B)$$ , where $$B\in\Lambda$$ , implies the isomorphism $$A\cong B$$ . The paper describes those Abelian groups in the class $$\mathscr Q\mathscr D_{\mathrm{cd}}$$ of completely decomposable quotient divisible Abelian groups which are determined by their endomorphism semigroups in the class $$\mathscr Q\mathscr D_{\mathrm{cd}}$$ .

中文翻译：

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具有同构内同态半群的完全可分解商可分阿贝尔群

令 $$\Lambda$$ 是一类阿贝尔群。如果每个同构 $$E^\star( A)\cong E^\star(B)$$ ，其中 $$B\in\Lambda$$ ，暗示同构 $$A\cong B$$ 。该论文描述了类 $$\mathscr Q\mathscr D_{\mathrm{cd}}$$ 中的完全可分解商可分阿贝尔群的那些阿贝尔群，它们由类 $$\mathscr Q\mathscr 中的自同态半群决定D_{\mathrm{cd}}$$ 。