  Do the Veronese rings of an algebra with straightening laws (ASL) still have
an ASL structure? We give positive answers to this question in some particular
cases, namely for the second Veronese algebra of Hibi rings and of discrete
ASLs. We also prove that the Veronese modules of the polynomial ring have a
structure of module with straightening laws. In dimension at most three we
present a poset construction that has the required combinatorial properties to
support such a structure.
