diff --git a/src/sage/categories/map.pyx b/src/sage/categories/map.pyx
index 5fd7637bc56..29988e2cba5 100644
--- a/src/sage/categories/map.pyx
+++ b/src/sage/categories/map.pyx
@@ -22,10 +22,11 @@ AUTHORS:
 #
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 from __future__ import print_function
 
 include "sage/ext/stdsage.pxi"
-import homset
+from . import homset
 import weakref
 from sage.structure.parent cimport Set_PythonType
 from sage.misc.constant_function import ConstantFunction
diff --git a/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx b/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx
index d7983d3dfb1..5e025302fe0 100644
--- a/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx
+++ b/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx
@@ -131,7 +131,7 @@ cdef class ntl_ZZ_pEContext_class(object):
         sage: c.ZZ_pE([4,3])
         [4 3]
         """
-        from ntl_ZZ_pE import ntl_ZZ_pE
+        from .ntl_ZZ_pE import ntl_ZZ_pE
         return ntl_ZZ_pE(v,modulus=self)
 
     def ZZ_pEX(self, v = None):
@@ -143,7 +143,7 @@ cdef class ntl_ZZ_pEContext_class(object):
         sage: c.ZZ_pEX([4,3])
         [[4] [3]]
         """
-        from ntl_ZZ_pEX import ntl_ZZ_pEX
+        from .ntl_ZZ_pEX import ntl_ZZ_pEX
         return ntl_ZZ_pEX(v, modulus=self)
 
 def ntl_ZZ_pEContext( ntl_ZZ_pX f):
diff --git a/src/sage/libs/ntl/ntl_mat_ZZ.pyx b/src/sage/libs/ntl/ntl_mat_ZZ.pyx
index bf27626ef34..1aac06904e2 100644
--- a/src/sage/libs/ntl/ntl_mat_ZZ.pyx
+++ b/src/sage/libs/ntl/ntl_mat_ZZ.pyx
@@ -20,7 +20,7 @@ from sage.libs.ntl.ntl_ZZ cimport ntl_ZZ
 from sage.libs.ntl.ntl_ZZX cimport ntl_ZZX
 from cpython.object cimport PyObject_RichCompare
 
-from ntl_ZZ import unpickle_class_args
+from .ntl_ZZ import unpickle_class_args
 
 cdef inline ntl_ZZ make_ZZ(ZZ_c* x):
     cdef ntl_ZZ y
diff --git a/src/sage/matrix/matrix_dense.pyx b/src/sage/matrix/matrix_dense.pyx
index a938cf59304..279752e42fa 100644
--- a/src/sage/matrix/matrix_dense.pyx
+++ b/src/sage/matrix/matrix_dense.pyx
@@ -7,11 +7,12 @@ TESTS::
     sage: m = matrix(R,2,[0,a,b,b^2])
     sage: TestSuite(m).run()
 """
+from __future__ import absolute_import
 from __future__ import print_function
 
-cimport matrix
+cimport sage.matrix.matrix as matrix
 
-from   sage.structure.element    cimport Element, RingElement
+from sage.structure.element cimport Element, RingElement
 from sage.structure.sage_object cimport richcmp_not_equal, rich_to_bool
 import sage.matrix.matrix_space
 import sage.structure.sequence
diff --git a/src/sage/matrix/matrix_generic_dense.pyx b/src/sage/matrix/matrix_generic_dense.pyx
index b87d09c67ed..76c19410a22 100644
--- a/src/sage/matrix/matrix_generic_dense.pyx
+++ b/src/sage/matrix/matrix_generic_dense.pyx
@@ -1,15 +1,17 @@
 """
 Dense Matrices over a general ring
 """
+from __future__ import absolute_import
+
 cimport cython
 from cpython.list cimport *
 from cpython.number cimport *
 from cpython.ref cimport *
 
-cimport matrix_dense
-import matrix_dense
+cimport sage.matrix.matrix_dense as matrix_dense
+from . import matrix_dense
 
-cimport matrix
+cimport sage.matrix.matrix as matrix
 
 from sage.structure.element cimport parent_c
 
diff --git a/src/sage/matrix/matrix_generic_sparse.pyx b/src/sage/matrix/matrix_generic_sparse.pyx
index aa6246fc265..4317088bea0 100644
--- a/src/sage/matrix/matrix_generic_sparse.pyx
+++ b/src/sage/matrix/matrix_generic_sparse.pyx
@@ -52,9 +52,10 @@ EXAMPLES::
     sage: c.is_sparse()
     True
 """
+from __future__ import absolute_import
 
-cimport matrix
-cimport matrix_sparse
+cimport sage.matrix.matrix as matrix
+cimport sage.matrix.matrix_sparse as matrix_sparse
 cimport sage.structure.element
 from sage.structure.element cimport ModuleElement
 
@@ -601,7 +602,6 @@ cdef class Matrix_generic_sparse(matrix_sparse.Matrix_sparse):
 ####################################################################################
 # Various helper functions
 ####################################################################################
-import matrix_space
 
 def Matrix_sparse_from_rows(X):
     """
@@ -633,6 +633,8 @@ def Matrix_sparse_from_rows(X):
         raise TypeError("X (=%s) must be a list or tuple"%X)
     if len(X) == 0:
         raise ArithmeticError("X must be nonempty")
+
+    from . import matrix_space
     entries = {}
     R = X[0].base_ring()
     ncols = X[0].degree()
diff --git a/src/sage/matrix/matrix_gf2e_dense.pyx b/src/sage/matrix/matrix_gf2e_dense.pyx
index a564fa377dd..61f79c8ae7c 100644
--- a/src/sage/matrix/matrix_gf2e_dense.pyx
+++ b/src/sage/matrix/matrix_gf2e_dense.pyx
@@ -74,10 +74,11 @@ REFERENCES:
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 
 include "cysignals/signals.pxi"
 
-cimport matrix_dense
+cimport sage.matrix.matrix_dense as matrix_dense
 from sage.structure.element cimport Matrix, Vector
 from sage.structure.element cimport ModuleElement, Element, RingElement
 
diff --git a/src/sage/matrix/matrix_mod2_dense.pyx b/src/sage/matrix/matrix_mod2_dense.pyx
index d1ca3a45777..d3cee44d392 100644
--- a/src/sage/matrix/matrix_mod2_dense.pyx
+++ b/src/sage/matrix/matrix_mod2_dense.pyx
@@ -99,11 +99,12 @@ TODO:
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 
 include "cysignals/signals.pxi"
 include "cysignals/memory.pxi"
 
-cimport matrix_dense
+cimport sage.matrix.matrix_dense as matrix_dense
 from libc.stdio cimport *
 from sage.structure.element cimport (Matrix, Vector, parent_c,
                                      ModuleElement, Element)
diff --git a/src/sage/matrix/matrix_sparse.pyx b/src/sage/matrix/matrix_sparse.pyx
index c928ee3f959..6147f2b8fdf 100644
--- a/src/sage/matrix/matrix_sparse.pyx
+++ b/src/sage/matrix/matrix_sparse.pyx
@@ -9,11 +9,12 @@ Base class for sparse matrices
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 from __future__ import print_function
 
 cimport cython
-cimport matrix
-cimport matrix0
+cimport sage.matrix.matrix as matrix
+cimport sage.matrix.matrix0 as matrix0
 from sage.structure.element cimport Element, RingElement, ModuleElement, Vector
 from sage.structure.sage_object cimport richcmp
 from sage.rings.ring import is_Ring
diff --git a/src/sage/modular/modsym/heilbronn.pyx b/src/sage/modular/modsym/heilbronn.pyx
index 732a5a1e123..d16541e372a 100644
--- a/src/sage/modular/modsym/heilbronn.pyx
+++ b/src/sage/modular/modsym/heilbronn.pyx
@@ -16,6 +16,7 @@ Heilbronn matrix computation
 #
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 
 import sage.arith.all
 
@@ -31,8 +32,8 @@ from sage.libs.flint.fmpz_poly cimport *
 cdef extern from "<math.h>":
     float roundf(float x)
 
-cimport p1list
-import  p1list
+cimport sage.modular.modsym.p1list as p1list
+from . import  p1list
 cdef p1list.export export
 export = p1list.export()
 
diff --git a/src/sage/modules/vector_integer_dense.pyx b/src/sage/modules/vector_integer_dense.pyx
index 549e2acc3d5..2424976cf35 100644
--- a/src/sage/modules/vector_integer_dense.pyx
+++ b/src/sage/modules/vector_integer_dense.pyx
@@ -52,7 +52,7 @@ TESTS::
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
-
+from __future__ import absolute_import
 
 include 'sage/ext/stdsage.pxi'
 
@@ -60,9 +60,9 @@ from sage.structure.element cimport Element, ModuleElement, RingElement, Vector
 
 from sage.rings.integer cimport Integer
 
-cimport free_module_element
+cimport sage.modules.free_module_element as free_module_element
 
-from free_module_element import vector
+from .free_module_element import vector
 
 from sage.libs.gmp.mpz cimport *
 
diff --git a/src/sage/modules/vector_mod2_dense.pyx b/src/sage/modules/vector_mod2_dense.pyx
index 6c7e913102a..9246fb47010 100644
--- a/src/sage/modules/vector_mod2_dense.pyx
+++ b/src/sage/modules/vector_mod2_dense.pyx
@@ -33,15 +33,15 @@ TESTS::
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
-
+from __future__ import absolute_import
 
 from sage.rings.finite_rings.integer_mod cimport IntegerMod_int, IntegerMod_abstract
 from sage.rings.integer cimport Integer
 from sage.rings.rational cimport Rational
 from sage.structure.element cimport Element, ModuleElement, RingElement, Vector
 
-cimport free_module_element
-from free_module_element import vector
+cimport sage.modules.free_module_element as free_module_element
+from .free_module_element import vector
 
 from sage.libs.m4ri cimport *
 
diff --git a/src/sage/modules/vector_modn_dense.pyx b/src/sage/modules/vector_modn_dense.pyx
index ea8d80276a7..230e2085af1 100644
--- a/src/sage/modules/vector_modn_dense.pyx
+++ b/src/sage/modules/vector_modn_dense.pyx
@@ -93,6 +93,7 @@ AUTHOR:
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 
 include "cysignals/memory.pxi"
 
@@ -114,8 +115,8 @@ cdef mod_int ivalue(IntegerMod_abstract x) except -1:
 
 from sage.structure.element cimport Element, ModuleElement, RingElement, Vector
 
-cimport free_module_element
-from free_module_element import vector
+cimport sage.modules.free_module_element as free_module_element
+from .free_module_element import vector
 
 cdef class Vector_modn_dense(free_module_element.FreeModuleElement):
     cdef _new_c(self):
diff --git a/src/sage/modules/vector_rational_dense.pyx b/src/sage/modules/vector_rational_dense.pyx
index 1023e90a271..6b78320a41b 100644
--- a/src/sage/modules/vector_rational_dense.pyx
+++ b/src/sage/modules/vector_rational_dense.pyx
@@ -50,6 +50,7 @@ TESTS::
 #  Distributed under the terms of the GNU General Public License (GPL)
 #                  http://www.gnu.org/licenses/
 ###############################################################################
+from __future__ import absolute_import
 from __future__ import print_function
 
 include "cysignals/signals.pxi"
@@ -60,8 +61,8 @@ from sage.structure.element cimport Element, ModuleElement, RingElement, Vector
 from sage.rings.integer cimport Integer
 from sage.rings.rational cimport Rational
 
-cimport free_module_element
-from free_module_element import vector
+cimport sage.modules.free_module_element as free_module_element
+from .free_module_element import vector
 
 from sage.libs.gmp.mpq cimport *
 
diff --git a/src/sage/structure/parent_base.pyx b/src/sage/structure/parent_base.pyx
index 0f5bb35ea03..7a7543bd687 100644
--- a/src/sage/structure/parent_base.pyx
+++ b/src/sage/structure/parent_base.pyx
@@ -8,12 +8,13 @@ Base class for old-style parent objects with a base ring
 #  The full text of the GPL is available at:
 #                  http://www.gnu.org/licenses/
 ###############################################################################
+from __future__ import absolute_import
 
 include "sage/ext/stdsage.pxi"
 
-cimport parent
+cimport sage.structure.parent as parent
 
-from coerce_exceptions import CoercionException
+from .coerce_exceptions import CoercionException
 
 cdef inline check_old_coerce(parent.Parent p):
     if p._element_constructor is not None:
diff --git a/src/sage/structure/parent_gens.pyx b/src/sage/structure/parent_gens.pyx
index 3f55fdd6e39..b64a4437f11 100644
--- a/src/sage/structure/parent_gens.pyx
+++ b/src/sage/structure/parent_gens.pyx
@@ -75,14 +75,15 @@ TESTS::
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+from __future__ import absolute_import
 from __future__ import print_function
 
 include 'sage/ext/stdsage.pxi'
 
 import sage.misc.defaults
 from sage.misc.latex import latex_variable_name
-import gens_py
-cimport parent
+from . import gens_py
+cimport sage.structure.parent as parent
 from sage.structure.coerce_dict import MonoDict
 cimport sage.structure.category_object as category_object
 
diff --git a/src/sage/structure/parent_old.pyx b/src/sage/structure/parent_old.pyx
index 6bcef821d71..ca6325bdef6 100644
--- a/src/sage/structure/parent_old.pyx
+++ b/src/sage/structure/parent_old.pyx
@@ -25,12 +25,13 @@ This came up in some subtle bug once.
 #  The full text of the GPL is available at:
 #                  http://www.gnu.org/licenses/
 ###############################################################################
+from __future__ import absolute_import
 from __future__ import print_function
 
-cimport sage_object
+cimport sage.structure.sage_object as sage_object
 import operator
-from parent import Set_PythonType, Set_PythonType_class
-from coerce import py_scalar_parent
+from .parent import Set_PythonType, Set_PythonType_class
+from .coerce import py_scalar_parent
 from sage.structure.coerce_dict import MonoDict, TripleDict
 
 from cpython.object cimport *