余代数K-理论(I):K_0群

Coalgebraic K-Theory I: K 0 Groups

本文在余代数上建立了相应的Ｋ０群，研究了Ｋ０函子对余代数的作用，得到了Ｋ０（σ）保持单同态的结构定理．文中给出了一系列余代数的Ｋ０群结构，尤其是在余交换的情形下，用Ｋ０群给出了余交换余代数不可约的一个充要条件．

In this paper we construct the K 0 group of coalgebra.We investigate the function K 0 and show that K 0(σ): K 0(D)→K 0(C) is injective provided that σ: C→D is injective and Corad(D)C. We also compute K 0 group of some coalgebras. We prove a sufficient and necessary condition for irreducible commutative coalgebra C is K 0(C)Z.