Ideal transforms and local cohomology defined by a pair of ideals

In this paper, we introduce a generalization of the ordinary ideal transform, denoted by DI,J, which is called the ideal transform with respect to a pair of ideals (I,J) and has an apparent algebraic structure. Then we study its various properties and explore the connection with the ordinary ideal transform. Also, we discuss the associated primes of local cohomology modules with respect to a pair of ideals. In particular, we give a characterization for the associated primes of the nonvanishing generalized local cohomology modules.