I have already had lunch.--为什么在already前要加"have",下面不行吗?

I have already had lunch.--为什么在already前要加"have",下面不行吗?
I already had lunch,--这句是不是语法不对啊,本人语法忘的差不多了.
I have already had lunch.
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现在完成时,不用加already也可以吧,这样不行吗:I have had lunch.