论文标题
兼容操作的克隆Z_ {p^k}}的克隆
Clones of Compatible Operations on Rings Z_{p^k}}
论文作者
论文摘要
我们研究了多项式函数克隆和保留函数的克隆之间的环Z_N上克隆的晶格I（n）。关键的情况是n是主要力量时。对于Prime P，晶格I（p）是微不足道的，I（p^2）是2元素的晶格。我们提供了i（p^3）的描述。为了实现这一结果，我们证明了一个还原定理，该定理说我（p^k）在z_p^（k-1）上的克隆晶格中是一定间隔。
We investigate the lattice I(n) of clones on the ring Z_n between the clone of polynomial functions and the clone of congruence preserving functions. The crucial case is when n is a prime power. For a prime p, the lattice I(p) is trivial and I(p^2) is known to be a 2-element lattice. We provide a description of I(p^3). To achieve this result, we prove a reduction theorem, which says that I(p^k) is isomorphic to a certain interval in the lattice of clones on Z_p^(k-1).
