Coderivations On Formal Triangular Matrix Coalgebras

As the dual concept of derivations in algebras,coderivations play an important role in studies of comodules and coalgebras.In this paper,we study the coderivations on coalgebras and comodules,provide the specific form of coderivation of the formal triangular matrix coalgebra(?).The main work of this paper is as follows:in the first part,we describe the relevant concept of derivations and coderivations,provide a construction of a standard complex and describe the relationship between low-order coderivations and cohomology groups,and the fundamental theorem on formal triangular matrix rings.In the second part,we describe some properties of coderivations and inner coderivations on comodules,and some fundamental properties and results.The third section is the main work and the innovative part of this paper,we establish the relationship between coderivations and relevant coalgebras,bicomodules on formal triangular matrix coalgebras in detail.