diff --git a/mihxil-algebra/src/main/java/org/meeuw/math/abstractalgebra/dihedral/DihedralGroup.java b/mihxil-algebra/src/main/java/org/meeuw/math/abstractalgebra/dihedral/DihedralGroup.java
index 202c8704..0fcd3ee2 100644
--- a/mihxil-algebra/src/main/java/org/meeuw/math/abstractalgebra/dihedral/DihedralGroup.java
+++ b/mihxil-algebra/src/main/java/org/meeuw/math/abstractalgebra/dihedral/DihedralGroup.java
@@ -20,11 +20,11 @@ public class DihedralGroup implements Group<DihedralSymmetry>, Streamable<Dihedr
     private DihedralGroup(int n) {
         this.n = n;
     }
+
     public static DihedralGroup of(int n) {
         return CACHE.computeIfAbsent(n, DihedralGroup::new);
     }
 
-
     public DihedralSymmetry r(int k) {
         return DihedralSymmetry.r(k, this);
     }
diff --git a/mihxil-algebra/src/main/java/org/meeuw/math/abstractalgebra/dihedral/DihedralSymmetry.java b/mihxil-algebra/src/main/java/org/meeuw/math/abstractalgebra/dihedral/DihedralSymmetry.java
index 7451c4c1..184593e9 100644
--- a/mihxil-algebra/src/main/java/org/meeuw/math/abstractalgebra/dihedral/DihedralSymmetry.java
+++ b/mihxil-algebra/src/main/java/org/meeuw/math/abstractalgebra/dihedral/DihedralSymmetry.java
@@ -25,11 +25,12 @@ public class DihedralSymmetry implements GroupElement<DihedralSymmetry>, UnaryOp
 
     private final DihedralGroup group;
 
-    static DihedralSymmetry r(int k, DihedralGroup diHedralGroup) {
-        return new DihedralSymmetry(r, k, diHedralGroup);
+    static DihedralSymmetry r(int k, DihedralGroup dihedralGroup) {
+        return new DihedralSymmetry(r, k, dihedralGroup);
     }
-    static DihedralSymmetry s(int k, DihedralGroup diHedralGroup) {
-        return new DihedralSymmetry(s, k, diHedralGroup);
+
+    static DihedralSymmetry s(int k, DihedralGroup dihedralGroup) {
+        return new DihedralSymmetry(s, k, dihedralGroup);
     }
 
     public static DihedralSymmetry r(int k, int n) {
@@ -41,17 +42,17 @@ public static DihedralSymmetry s(int k, int n) {
     }
 
 
-    private DihedralSymmetry(Symmetry symmetry, int k, DihedralGroup diHedralGroup) {
+    private DihedralSymmetry(Symmetry symmetry, int k, DihedralGroup dihedralGroup) {
         this.symmetry = symmetry;
         if (k < 0) {
             throw new InvalidElementCreationException(symmetry.name() + k + " is impossible");
         }
         this.k = k;
-        if (k >= diHedralGroup.n) {
-            throw new InvalidElementCreationException(symmetry.name() + k + " is impossible for " + diHedralGroup);
+        if (k >= dihedralGroup.n) {
+            throw new InvalidElementCreationException(symmetry.name() + k + " is impossible for " + dihedralGroup);
 
         }
-        this.group = diHedralGroup;
+        this.group = dihedralGroup;
     }
 
     private DihedralSymmetry(Symmetry symmetry, int k, int n) {
diff --git a/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/MultiplicativeMonoidElement.java b/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/MultiplicativeMonoidElement.java
index 388595d1..8db00e34 100644
--- a/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/MultiplicativeMonoidElement.java
+++ b/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/MultiplicativeMonoidElement.java
@@ -17,7 +17,7 @@
 
 import jakarta.validation.constraints.Min;
 
-import org.meeuw.math.exceptions.ReciprocalException;
+import org.meeuw.math.exceptions.IllegalPowerException;
 
 /**
  * An element of the {@link MultiplicativeMonoid} structure.
@@ -39,7 +39,7 @@ public interface MultiplicativeMonoidElement<E extends MultiplicativeMonoidEleme
     @Override
     default E pow(@Min(0) int n) {
         if (n < 0) {
-            throw new ReciprocalException("");
+            throw new IllegalPowerException("");
         }
         if (n == 0) {
             return getStructure().one();
diff --git a/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/Ring.java b/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/Ring.java
index 9a9012ce..61b1c1d3 100644
--- a/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/Ring.java
+++ b/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/Ring.java
@@ -15,8 +15,12 @@
  */
 package org.meeuw.math.abstractalgebra;
 
+import java.util.NavigableSet;
+
 import org.checkerframework.checker.nullness.qual.NonNull;
 import org.meeuw.math.ArrayUtils;
+import org.meeuw.math.operators.AlgebraicBinaryOperator;
+import org.meeuw.math.operators.AlgebraicUnaryOperator;
 import org.meeuw.math.validation.Square;
 
 import static org.meeuw.math.ArrayUtils.minor;
@@ -28,9 +32,12 @@
  * @since 0.4
  * @param <E>
  */
-public interface Ring<E extends RingElement<E>> extends Rng<E> {
+public interface Ring<E extends RingElement<E>> extends Rng<E>, MultiplicativeMonoid<E> {
+
+
+    NavigableSet<AlgebraicBinaryOperator> OPERATORS = Rng.OPERATORS;
+    NavigableSet<AlgebraicUnaryOperator> UNARY_OPERATORS = Rng.UNARY_OPERATORS;
 
-    E one();
 
      /**
      * Given a (square) matrix of elements of this Ring, calculate its determinant.
diff --git a/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/RingElement.java b/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/RingElement.java
index 8ff1fbcf..f28ff391 100644
--- a/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/RingElement.java
+++ b/mihxil-math/src/main/java/org/meeuw/math/abstractalgebra/RingElement.java
@@ -20,7 +20,7 @@
  * @author Michiel Meeuwissen
  * @since 0.4
  */
-public interface RingElement<E extends RingElement<E>> extends RngElement<E> {
+public interface RingElement<E extends RingElement<E>> extends RngElement<E>, MultiplicativeMonoidElement<E> {
 
     @Override
     Ring<E> getStructure();
diff --git a/mihxil-theories/src/main/java/org/meeuw/theories/abstractalgebra/DivisionRingTheory.java b/mihxil-theories/src/main/java/org/meeuw/theories/abstractalgebra/DivisionRingTheory.java
index 0fcfe011..5eb3db57 100644
--- a/mihxil-theories/src/main/java/org/meeuw/theories/abstractalgebra/DivisionRingTheory.java
+++ b/mihxil-theories/src/main/java/org/meeuw/theories/abstractalgebra/DivisionRingTheory.java
@@ -31,6 +31,7 @@
  * @since 0.4
  */
 public interface DivisionRingTheory<E extends DivisionRingElement<E>> extends
+    RingTheory<E>,
     MultiplicativeGroupTheory<E>,
     AdditiveGroupTheory<E>  {
 
@@ -54,15 +55,4 @@ default void operatorEnums(
             .isEqualTo((e1.plus(e2).sqr()).negation());
     }
 
-    @Property
-    default void distributivity (
-        @ForAll(ELEMENTS) E v1,
-        @ForAll(ELEMENTS) E v2,
-        @ForAll(ELEMENTS) E v3
-    ) {
-        assertThat(v1.times(v2.plus(v3)))
-            .usingComparator(eqComparator())
-            .isEqualTo(v1.times(v2).plus(v1.times(v3)));
-    }
-
 }
diff --git a/mihxil-theories/src/main/java/org/meeuw/theories/abstractalgebra/RingTheory.java b/mihxil-theories/src/main/java/org/meeuw/theories/abstractalgebra/RingTheory.java
index 8f749c0d..3739e249 100644
--- a/mihxil-theories/src/main/java/org/meeuw/theories/abstractalgebra/RingTheory.java
+++ b/mihxil-theories/src/main/java/org/meeuw/theories/abstractalgebra/RingTheory.java
@@ -21,16 +21,28 @@
 import org.meeuw.math.abstractalgebra.RingElement;
 
 import static org.assertj.core.api.Assertions.assertThat;
+import static org.meeuw.math.abstractalgebra.AlgebraicElement.eqComparator;
 
 /**
  * @author Michiel Meeuwissen
  * @since 0.4
  */
-public interface RingTheory<E extends RingElement<E>> extends AdditiveGroupTheory<E>, RngTheory<E> {
+public interface RingTheory<E extends RingElement<E>> extends AdditiveGroupTheory<E>, RngTheory<E> , MultiplicativeMonoidTheory<E> {
 
     @Property
     default void one(
         @ForAll(ELEMENTS) E v) {
         assertThat(v.times(v.getStructure().one())).isEqualTo(v);
     }
+
+    @Property
+    default void distributivity (
+        @ForAll(ELEMENTS) E v1,
+        @ForAll(ELEMENTS) E v2,
+        @ForAll(ELEMENTS) E v3
+    ) {
+        assertThat(v1.times(v2.plus(v3)))
+            .usingComparator(eqComparator())
+            .isEqualTo(v1.times(v2).plus(v1.times(v3)));
+    }
 }