Recently in [Vij09, Corollary 3.7] the complexity class ModL has been shown to be closed under complement assuming NL = UL. In this note we continue to show many other closure properties of ModL which include the following.
1. ModL is closed under \leq ^L_m reduction, \vee(join) and \leq ^{UL}_m reduction,
m reduction
2. ModL is closed under \leq ^L_{1-tt} and \leq ^{UL}_{1-tt} reduction assuming NL =
UL,
3. ModL^{UL}=ModL assuming UL=coUL,
4. UL^{ModL}_{1-tt}=ModL^{UL}=ModL assuming NL = UL,
5. if l\in Z^{+} such that l\geq 2 and ModL is closed under \leq ^L_{l-dtt} reduction then Mod_kL\subseteq ModL for all k\in Z^{+} such that k\geq 6 is a composite
number and k has at least 2 and at most l distinct prime divisors, and
6. if ModL is closed under \leq ^L_{dtt} reduction then coC=L\subseteq ModL.
Also using [Vij09, Corollary 3.7] we show that if NL = UL and ModL is closed under \leq ^L_{ l-dtt} and \leq ^L_{dtt} reduction then ModL is also closed under \leq ^L_{1-ctt} and \leq ^L_{ctt}$ reduction respectively.
We also show a proof of the well known result that the determinant of a matrix with entries in Z is computable in L-uniform TC1 from which it follows that ModL\subseteqL-uniform TC1.