Package org.meeuw.math.abstractalgebra
Interface DivisionRing<E extends DivisionRingElement<E>>
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- All Superinterfaces:
AdditiveAbelianGroup<E>,AdditiveGroup<E>,AdditiveMonoid<E>,AdditiveSemiGroup<E>,AlgebraicStructure<E>,MultiplicativeGroup<E>,MultiplicativeMonoid<E>,MultiplicativeSemiGroup<E>,Ring<E>,Rng<E>
- All Known Subinterfaces:
CompleteField<E>,Field<E>,ScalarField<E>
- All Known Implementing Classes:
UncertainRealField
public interface DivisionRing<E extends DivisionRingElement<E>> extends MultiplicativeGroup<E>, Ring<E>
A division ring is a ring, where also the multiplicative inverse is defined, but where multiplication is not necessarily commutative. In other words it is 'skewed field', or non-commutative field.- Since:
- 0.4
- Author:
- Michiel Meeuwissen
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Field Summary
Fields Modifier and Type Field Description static Set<Operator>OPERATORS-
Fields inherited from interface org.meeuw.math.abstractalgebra.AdditiveSemiGroup
UNARY_OPERATORS
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Method Summary
All Methods Instance Methods Default Methods Modifier and Type Method Description default Set<Operator>getSupportedOperators()Returns theOperators that elements of this structure support.-
Methods inherited from interface org.meeuw.math.abstractalgebra.AdditiveMonoid
zero
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Methods inherited from interface org.meeuw.math.abstractalgebra.AdditiveSemiGroup
getSupportedUnaryOperators
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Methods inherited from interface org.meeuw.math.abstractalgebra.AlgebraicStructure
getCardinality, getDescription, getElementClass, getEquivalence
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Methods inherited from interface org.meeuw.math.abstractalgebra.MultiplicativeMonoid
one
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Method Detail
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getSupportedOperators
default Set<Operator> getSupportedOperators()
Description copied from interface:AlgebraicStructureReturns theOperators that elements of this structure support.- Specified by:
getSupportedOperatorsin interfaceAdditiveGroup<E extends DivisionRingElement<E>>- Specified by:
getSupportedOperatorsin interfaceAdditiveSemiGroup<E extends DivisionRingElement<E>>- Specified by:
getSupportedOperatorsin interfaceAlgebraicStructure<E extends DivisionRingElement<E>>- Specified by:
getSupportedOperatorsin interfaceMultiplicativeGroup<E extends DivisionRingElement<E>>- Specified by:
getSupportedOperatorsin interfaceMultiplicativeSemiGroup<E extends DivisionRingElement<E>>- Specified by:
getSupportedOperatorsin interfaceRng<E extends DivisionRingElement<E>>
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