On the $\mathrm{UA}$-properties of Abelian $sp$-groups and their endomorphism rings

An $R$-module $A$ is said to be a $\mathrm{UA}$-module if it is not possible to change the addition of $A$ without changing the action of $R$ on $A$. A semigroup $(R,\cdot)$ is said to be a $\mathrm{UA}$-ring if there exists a unique binary operation $+$ making $(R,\cdot,+)$ into a ring. In this paper, the $\mathrm{UA}$-properties of $sp$-groups and their endomorphism rings are studied.