Inside an a4j:form, I have an a h:inputText, an a4j:commandButton and a rich:dataTable.
<a4j:form id="form1">
<h:inputText value="${someBean.s}" required="true" id="name"/><h:message for="form1:name"/>
<a4j:commandButton value="Add" action="${someBean.add}" reRender="form1:dataTable"/>
<rich:dataTable id="dataTable" .....>
</a4j:form>