commutative rings and division rings; type punning.

src/main/java/rocks/palaiologos/maja/structure/CommutativeRing.java

@@ -0,0 +1,8 @@
+package rocks.palaiologos.maja.structure;
+
+/**
+ * A division ring is a set R equipped with two binary operations + and ·, where (R, +) and (R, ·) are abelian groups.
+ * The multiplication distributes over addition (left and right distributivity).
+ */
+public interface CommutativeRing<T> extends AdditiveAbelianGroup<T>, MultiplicativeAbelianGroup<T> {
+}

src/main/java/rocks/palaiologos/maja/structure/DivisionRing.java

@@ -0,0 +1,8 @@
+package rocks.palaiologos.maja.structure;
+
+/**
+ * A division ring is a set R equipped with two binary operations + and ·, where (R, +) is an abelian group and (R, ·) is a group.
+ * The multiplication distributes over addition (left and right distributivity).
+ */
+public interface DivisionRing<T> extends AdditiveAbelianGroup<T>, MultiplicativeGroup<T> {
+}

src/main/java/rocks/palaiologos/maja/structure/Ring.java

@@ -5,4 +5,90 @@
  * The multiplication distributes over addition (left and right distributivity).
  */
 public interface Ring<T> extends AdditiveAbelianGroup<T>, MultiplicativeMonoid<T> {
+    static <T> Ring<T> of(DivisionRing<T> divisionRing) {
+        return new Ring<T>() {
+            @Override
+            public T addInv(T a) {
+                return divisionRing.addInv(a);
+            }
+
+            @Override
+            public T zero() {
+                return divisionRing.zero();
+            }
+
+            @Override
+            public T plus(T a, T b) {
+                return divisionRing.plus(a, b);
+            }
+
+            @Override
+            public T one() {
+                return divisionRing.one();
+            }
+
+            @Override
+            public T dot(T a, T b) {
+                return divisionRing.dot(a, b);
+            }
+        };
+    }
+
+    static <T> Ring<T> of(CommutativeRing<T> commutativeRing) {
+        return new Ring<T>() {
+            @Override
+            public T addInv(T a) {
+                return commutativeRing.addInv(a);
+            }
+
+            @Override
+            public T zero() {
+                return commutativeRing.zero();
+            }
+
+            @Override
+            public T plus(T a, T b) {
+                return commutativeRing.plus(a, b);
+            }
+
+            @Override
+            public T one() {
+                return commutativeRing.one();
+            }
+
+            @Override
+            public T dot(T a, T b) {
+                return commutativeRing.dot(a, b);
+            }
+        };
+    }
+
+    static <T> Ring<T> of(AdditiveAbelianGroup<T> additiveAbelianGroup, MultiplicativeMonoid<T> multiplicativeMonoid) {
+        return new Ring<T>() {
+            @Override
+            public T addInv(T a) {
+                return additiveAbelianGroup.addInv(a);
+            }
+
+            @Override
+            public T zero() {
+                return additiveAbelianGroup.zero();
+            }
+
+            @Override
+            public T plus(T a, T b) {
+                return additiveAbelianGroup.plus(a, b);
+            }
+
+            @Override
+            public T one() {
+                return multiplicativeMonoid.one();
+            }
+
+            @Override
+            public T dot(T a, T b) {
+                return multiplicativeMonoid.dot(a, b);
+            }
+        };
+    }
 }