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In this sentence "He bought a new lamp for the bike", is "a new lamp" the direct object and "for the bike" the indirect object? Or is the indirect object always a person?

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SanTwoIn this sentence "He bought a new lamp for the bike", is "a new lamp" the direct object

Yes.

SanTwoand "for the bike" the indirect object?

No.

SanTwo is the indirect object always a person?

No.

I gave my dog a bath.

I bought my car new seat covers.