有限环上的齐次重量与Mbius函数

Homogeneous Weights and Mbius Functions on Finite Rings

讨论了有限环上齐次重量、M(o|¨)bius函数和欧拉phi-函数等函数之间的关系.在有限主理想环上给出了这些函数的易于计算的刻画,对于整数剩余类环把它们还原成了经典的数论M(o|¨)bius函数和数论欧拉phi-函数.

The relations among the homogeneous weights,the Mobius functions and Euler phi-functions on finite rings are discussed.Some computational formulas for these functions on finite principal ideal rings are characterized.For the residue rings of integers,they are reduced to the classical number-theoretical Mobius functions and the classical number-theoretical Euler phi-functions.