Nonaqueous electrolyte, its manufacturing method, the positive electrode active material is used f

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An object of the present invention is to provide a positive electrode active material for a nonaqueous electrolyte secondary battery etc. which are capable of suppressing a reaction between a positive electrode and an electrolyte decomposition product moved from a negative electrode and a reaction between the positive electrode and the electrolyte, and which are thereby capable of significantly improving battery characteristics such as continuous charge characteristics (particularly, continuous charge characteristics at a high temperature), cycling characteristics, etc. The positive electrode active material includes a compound containing a rare earth element and fluorine and adhered to a surface of a lithium transition metal composite oxide, the compound having an average particle diameter of 1 nm or less and 100 nm or more.