AJAX发布现场完成？

I have the code below that validates a form field called lms_domain. It simply checks whether the subdomain selected by the user is available using an AJAX call to another file that executes a MySQLi count query. The code currently works on submission of the form but I would like it to execute the AJAX post when the user types into the field, or has completed the field. How do you achieve this using JQuery?

$('#lms_name').keyup(function(){

    /* some code here */

    $.ajax({
        type: 'POST',
        url: 'assets/lmsdomaincheck.php',
        data: "lmsdomain="+value+".thedomain.com",
        async: false,
        success: function(htmldata){

            if (htmldata=="success") {
                $('#spanlmsdomain').html('GOOD');
            }else {
                msg+="<b>Error on LMS domain name : </b>"+value+".thedomain.com not available.<br/>";
                $('#spanlmsdomain').html('BAD');
            }
        }
    });

    /* some code here */

});

Thanks in advance for any tips!