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Should I include a professor's name in my paper to get it published?

I am a master's student and want to publish a paper in a specific subfield in mathematics. I have written the paper all by myself.

The problem is my advisor won't check my draft. He says he is busy and so he could not find time.

My question is:

  • When papers are submitted to reviewers and editors, do they see what are the names of the authors in the paper submitted?

  • If my professor co-authors a paper will it be easier to get published?

  • Should I include my professor's name with my name to get the paper published easier?

I really want to publish it with my name only. But I really don't know how this publication process works.

user96599