Add Product SKU on shop and category pages

functions.php

function woocommerce_after_shop_loop_item_title_short_description() { 
   global $product; 
   if ( ! $product->get_sku() ) return;
   ?> <div itemprop="description"> 
      <?php echo apply_filters( 'woocommerce_short_description', $product->get_sku() ) ?> </div> 
   <?php 
} 

add_action('woocommerce_after_shop_loop_item_title', 'woocommerce_after_shop_loop_item_title_short_description', 5);