diff --git a/Kinetic_data_structures/include/CGAL/Polynomial/basic.h b/Kinetic_data_structures/include/CGAL/Polynomial/basic.h
index a8bfdba9c9b..d9ff4ccf448 100644
--- a/Kinetic_data_structures/include/CGAL/Polynomial/basic.h
+++ b/Kinetic_data_structures/include/CGAL/Polynomial/basic.h
@@ -91,10 +91,10 @@ Sign sign(const NT &nt)
 }
 
 
-typedef ::CGAL::Ring_tag             Ring_tag;
+typedef ::CGAL::Integral_domain_without_division_tag             Integral_domain_without_division_tag;
 typedef ::CGAL::Euclidean_ring_tag   Euclidean_ring_tag;
 typedef ::CGAL::Field_tag            Field_tag;
-typedef ::CGAL::Sqrt_field_tag       Sqrt_field_tag;
+typedef ::CGAL::Field_with_sqrt_tag       Field_with_sqrt_tag;
 
 CGAL_POLYNOMIAL_END_NAMESPACE
 
@@ -127,10 +127,10 @@ Sign sign(const NT &nt)
 }
 
 
-struct Ring_tag {};
+struct Integral_domain_without_division_tag {};
 struct Euclidean_ring_tag {};
 struct Field_tag {};
-struct Sqrt_field_tag {};
+struct Field_with_sqrt_tag {};
 
 CGAL_POLYNOMIAL_END_NAMESPACE
 #endif
diff --git a/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Compare_isolated_roots_in_interval.h b/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Compare_isolated_roots_in_interval.h
index 47f207fee9f..e26ff1d5564 100644
--- a/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Compare_isolated_roots_in_interval.h
+++ b/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Compare_isolated_roots_in_interval.h
@@ -25,7 +25,7 @@
 
 CGAL_POLYNOMIAL_BEGIN_INTERNAL_NAMESPACE
 
-template<class Kernel, class M = CGAL::Ring_tag>
+template<class Kernel, class M = CGAL::Integral_domain_without_division_tag>
 class Compare_isolated_roots_in_interval
 {
     protected:
diff --git a/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Root_bound_evaluator.h b/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Root_bound_evaluator.h
index c8f9a5b02e7..b4161b60152 100644
--- a/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Root_bound_evaluator.h
+++ b/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Root_bound_evaluator.h
@@ -51,7 +51,7 @@ class Root_bound_evaluator
 
         static NT
             compute_bound(const NT& max_abs, const NT& abs_lead_cf,
-        CGAL::Ring_tag) {
+        CGAL::Integral_domain_without_division_tag) {
 #if 1
             double d1 = to_double(max_abs);
             double d2 = to_double(abs_lead_cf);
@@ -128,7 +128,7 @@ class Filtered_root_bound_evaluator
         template <class NTT>
             static NTT
             compute_bound(const NTT& max_abs, const NTT& abs_lead_cf,
-        CGAL::Ring_tag) {
+        CGAL::Integral_domain_without_division_tag) {
 #if 1
             double d1 = CGAL::to_double(max_abs);
             double d2 = CGAL::to_double(abs_lead_cf);
diff --git a/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Standard_sequence.h b/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Standard_sequence.h
index e4b68d03df0..d00adb54f5f 100644
--- a/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Standard_sequence.h
+++ b/Kinetic_data_structures/include/CGAL/Polynomial/internal/Rational/Standard_sequence.h
@@ -72,7 +72,7 @@ class Standard_sequence : public Sturm_sequence_t
 };
 
 #if 0
-template<class Kernel, class Ret, class M = CGAL::Ring_tag>
+template<class Kernel, class Ret, class M = CGAL::Integral_domain_without_division_tag>
 class Standard_sequence_k
 : public Sturm_sequence_k<Kernel, Ret,M>
 {
diff --git a/Kinetic_data_structures/include/CGAL/Polynomial/internal/Sturm_root_rep.h b/Kinetic_data_structures/include/CGAL/Polynomial/internal/Sturm_root_rep.h
index 5cf5569847c..4ea4390af56 100644
--- a/Kinetic_data_structures/include/CGAL/Polynomial/internal/Sturm_root_rep.h
+++ b/Kinetic_data_structures/include/CGAL/Polynomial/internal/Sturm_root_rep.h
@@ -624,7 +624,7 @@ public:
   }
 #if 1
   template<class Child>
-  Polynomial compute_simple(Ring_tag, const Child&) const
+  Polynomial compute_simple(Integral_domain_without_division_tag, const Child&) const
   {
     Polynomial gcd = sseq.exact( sseq.exact_size() - 1 );
     return p_.pseudo_quotient( gcd );
@@ -637,7 +637,7 @@ public:
     return p_ / gcd;
   }
 #endif
-  Polynomial compute_simple(Ring_tag, const Self&) const
+  Polynomial compute_simple(Integral_domain_without_division_tag, const Self&) const
   {
     Polynomial gcd = sseq[sseq.size() - 1];
     return tr_.pseudo_quotient_object()(p_, gcd);