环Z_{p^k}上相容运算的克隆
Clones of Compatible Operations on Rings Z_{p^k}}
摘要：
研究了环Z_n上多项式函数克隆与保同余函数克隆之间的克隆格I（n）.关键的情况是当n是素数幂时。对于素数p，格I（p）是平凡的，并且已知I（p^2）是2元格。我们给出了I（p^3）的描述。为了达到这个结果，我们证明了一个约化定理，即I（p^k）同构于Z_p^（k-1）上克隆格中的某个区间。
英文摘要：
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).
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