diff --git a/heat/core/dndarray.py b/heat/core/dndarray.py
index 5f17f3ba5c..8cf1dff2cc 100644
--- a/heat/core/dndarray.py
+++ b/heat/core/dndarray.py
@@ -56,6 +56,8 @@ def __init__(
         comm: Communication,
         balanced: bool,
     ):
+        dtype = types.canonical_heat_type(dtype)
+
         self.__array = array
         self.__gshape = gshape
         self.__dtype = dtype
@@ -69,8 +71,17 @@ def __init__(
         self.__partitions_dict__ = None
         self.__lshape_map = None
 
-        # check for inconsistencies between torch and heat devices
+        # check for inconsistencies between local and global arrays
         assert str(array.device) == device.torch_device
+        assert self.ndim == array.ndim, (
+            f"Local dimension {array.ndim} exceeds global dimension {self.ndim}!"
+        )
+        assert all([gshape[i] >= array.shape[i] for i in range(self.ndim)]), (
+            f"Local shape {array.shape} is larger than global shape {gshape}"
+        )
+        assert dtype == types.canonical_heat_type(array.dtype), (
+            f"Local datatype {array.dtype} is incompatible with global datatype {dtype}"
+        )
 
     @property
     def balanced(self) -> bool: