session on the application web

I want to create an application Web PHP/mysql. my problem is that the
application must retain some information as the name of the user. each
information is created by a given user and the right to modify is
authorized to only this user, the others have right to only consult.
problem to retain the name of user and to compare it with the name of
creator which is reproduced on the table of the base of data. thank you