标题： 将周期群的拟变体的嵌入格嵌入到加法幂等半环种类的格中：代数证明 显示英文标题

标题： Embedding lattices of quasivarieties of periodic groups into lattices of additively idempotent semiring varieties: An algebraic proof

摘要： 一个由Jackson得出的普遍结果（Flat algebras and the translation of universal Horn logic to equational logic, J. Symb. Log. 73(1) (2008) 90--128）表明，所有指数整除$n$的群的拟 varieties 的格嵌入到所有加法幂等半环的种类格$L(\mathbf{Sr}_n)$中，其乘法半群是指数整除$n$的群的并集；该嵌入的像是$L(\mathbf{Sr}_n)$中的一个区间。我们提供了这些事实的新、直接且纯粹代数的证明，并给出了该区间的最上层种类的新恒等式基。 此外，我们获得了关于格子$L(\mathbf{Sr}_n)$的新信息，表明当$n\ge 3$时，该格子的性质与之前已知的$n=1$或$2$的性质有显著不同。 显示英文摘要

摘要： A general result by Jackson (Flat algebras and the translation of universal Horn logic to equational logic, J. Symb. Log. 73(1) (2008) 90--128) implies that the lattice of all quasivarieties of groups of exponent dividing $n$ embeds into the lattice $L(\mathbf{Sr}_n)$ of all varieties of additively idempotent semirings whose multiplicative semigroups are unions of groups of exponent dividing $n$; the image of this embedding is an interval in $L(\mathbf{Sr}_n)$. We provide a new, direct, and purely algebraic proof of these facts and present a new identity basis for the top variety of the interval. In addition, we obtain new information about the lattice $L(\mathbf{Sr}_n)$, demonstrating that the properties of the lattice for $n\ge 3$ differ drastically from those previously known when $n=1$ or $2$.