<!DOCTYPE html>
<style>
.outer {
    text-decoration: underline;
}
.middle {
    position: absolute;
    top: 50px;
}
.inner {
    text-decoration: none;
}

.override {
    position: static;
}
</style>
<div class="outer">
  <div class="middle">
    This text should not inherit text-decoration from its parent, and should therefore not be underlined. 
    <p>
    <a href="www.example.com" class="inner">As the child of an absolutely positioned block, this link should not be underlined</a>
  </div>
</div>
<div class="outer">
  <div class="middle override">
    <a href="www.example.com" class="inner">As the child of a statically positioned block, this link should be underlined</a>
  </div>
</div>