Prevent duplicate Account using Trigger

This is the trigger i have wrote to prevent the creation of duplicate Accounts based on Account Name.

trigger preventDuplicateAccount on Account(before insert,before update){

set<string> accountSet = new set<string>(); 

Map<string,Account> accountMap = new Map<string,Account>();

for(Account ac:trigger.new){

    accountSet.add(ac.name);

}

for(Account a:[SELECT id,name from Account where Name IN :accountSet]){

     accountMap.put(a.Name,a);

}

for(Account account:trigger.new){

    if(accountMap.containsKey(account.name)  ){

       //show error msg on the Account Name field

         account.Name.addError('Account is Already Exist');

       }

}

}