Simple PHP script - what have I missed?

PHP
1

Trying to build a simple WordPress widget plugin, I am stuck on a simple select box:

<?php
class wp_my_plugin extends WP_Widget {

    // constructor
    function wp_my_plugin() {
        parent::WP_Widget(false, $name = __('Select Test', 'wp_my_plugin') );
    }

    // widget form creation
function form($instance) {

// Check values
if( $instance) {
    $select = esc_attr($instance['select']);
} else {
    $select = '';
}
?>

<p>
<label for="<?php echo $this->get_field_id('select'); ?>"><?php _e('Select', 'wp_widget_plugin'); ?></label>
<select name="<?php echo $this->get_field_name('select'); ?>" id="<?php echo $this->get_field_id('select'); ?>" class="widefat">
<?php
$options = array('lorem', 'ipsum', 'dolorem');
foreach ($options as $option) {
echo '<option value="' . $option . '" id="' . $option . '"', $select == $option ? ' selected="selected"' : '', '>', $option, '</option>';
}
?>
</select>
</p>

<?php
}

    // update widget
function update($new_instance, $old_instance) {
      $instance = $old_instance;
      // Fields
      $instance['select'] = strip_tags($new_instance['select']);
    return $instance;
}

    // display widget
function widget($args, $instance) {
  extract( $args );
  // these are the widget options
  $select = $select['select'];

  echo $before_widget;
  // Display the widget
  echo '<div class="widget-text wp_widget_plugin_box">';

  // Get $select value
    if ( $select == 'lorem' ) {
        echo 'Lorem option is Selected';
        } else if ( $select == 'ipsum' ) {
        echo 'ipsum option is Selected';
        } else {
        echo 'dolorem option is Selected';
    }

  echo '</div>';
  echo $after_widget;
}
}
// register widget
add_action('widgets_init', create_function('', 'return register_widget("wp_my_plugin");'));

Can anyone see what I have missed? $select is showing blank…