diff --git a/semiring-num.cabal b/semiring-num.cabal
--- a/semiring-num.cabal
+++ b/semiring-num.cabal
@@ -1,5 +1,5 @@
 name:                semiring-num
-version:             0.1.0.5
+version:             0.1.0.6
 synopsis:            Basic semiring class and instances
 description:         Adds a basic semiring class
 homepage:            https://github.com/oisdk/semiring-num
diff --git a/src/Data/Semiring.hs b/src/Data/Semiring.hs
--- a/src/Data/Semiring.hs
+++ b/src/Data/Semiring.hs
@@ -71,9 +71,7 @@
 -- * @a '<.>' (b '<+>' c) = (a '<.>' b) '<+>' (a '<.>' c)@
 -- * @(a '<+>' b) '<.>' c = (a '<.>' c) '<+>' (b '<.>' c)@
 --
--- Another useful law, annihilation, may be deduced from the axioms
--- above:
---
+-- == Annihilation
 -- * @'zero' '<.>' a = a '<.>' 'zero' = 'zero'@
 class Semiring a where
   -- | The identity of '<+>'.
diff --git a/src/Data/Semiring/Free.hs b/src/Data/Semiring/Free.hs
--- a/src/Data/Semiring/Free.hs
+++ b/src/Data/Semiring/Free.hs
@@ -4,6 +4,7 @@
 {-# LANGUAGE DeriveTraversable          #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
 
+-- | The Free semiring.
 module Data.Semiring.Free
   ( Free(..)
   , liftFree
diff --git a/src/Test/Semiring.hs b/src/Test/Semiring.hs
--- a/src/Test/Semiring.hs
+++ b/src/Test/Semiring.hs
@@ -16,6 +16,7 @@
   , mulDistribR
   , plusId
   , mulId
+  , annihilate
   , semiringLaws
   ) where
 
@@ -88,7 +89,7 @@
     , "(x <+> y) <.> z = " ++ show l
     , "x <.> z <+> y <.> z = " ++ show r ]
 
--- | Additive identity
+-- | Additive identity.
 plusId :: (Eq a, Semiring a, Show a) => a -> Property
 plusId x = counterexample s (l == x && r ==x) where
   l = x <+> zero
@@ -100,7 +101,7 @@
     , "x <+> zero = " ++ show l
     , "zero <+> x = " ++ show r ]
 
--- | Multiplicative identity
+-- | Multiplicative identity.
 mulId :: (Eq a, Semiring a, Show a) => a -> Property
 mulId x = counterexample s (l == x && r ==x) where
   l = x <.> one
@@ -112,6 +113,18 @@
     , "x <.> one = " ++ show l
     , "one <.> x = " ++ show r ]
 
+-- | Annihilation of '<.>' by 'zero'.
+annihilate :: (Eq a, Semiring a, Show a) => a -> Property
+annihilate x = counterexample s (l == zero && r == zero) where
+  l = x <.> zero
+  r = zero <.> x
+  s = unlines
+    [ "Testing annihilation of <.> by zero."
+    , "Law: x <.> zero = zero <.> x = zero"
+    , "x = " ++ show x
+    , "x <.> zero = " ++ show l
+    , "zero <.> x = " ++ show r ]
+
 -- | A property for all laws of 'Semiring'.
 semiringLaws :: (Eq a, Semiring a, Show a, Arbitrary a) => Proxy a -> Property
 semiringLaws (_ :: Proxy a) = conjoin
@@ -121,4 +134,5 @@
   , property (mulDistribL :: a -> a -> a -> Property)
   , property (mulDistribR :: a -> a -> a -> Property)
   , property (plusId      ::           a -> Property)
-  , property (mulId       ::           a -> Property)]
+  , property (mulId       ::           a -> Property)
+  , property (annihilate  ::           a -> Property)]