Abstract: We considered the characterization problem of weighted right core inverses and weighted right pseudo core inverses over *-rings by 
using algebraic methods. Firstly, the concept of weighted right core inverse was introduced. Secondly,  three equations and right invertible elements were used to give its characterization. Finally, the definition and characterization of weighted right pseudo core inverse were given.

Key words: core inverse, weighted core inverse, weighted pseudo core inverse, right core inverse, weighted right core inverse, weighted right pseudo core inverse