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An additive subgroup of a ring such that and lie in for every and ; for commutative rings the two absorption conditions coincide.
stacks-algebra-textmilne-algebraic-number-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Ideals of a commutative ring are additive subgroups closed under multiplication by arbitrary ring elements, providing the compatible equivalence data used in quotient rings.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
stacks-algebra-textEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Prime ideals are the proper ideals for which a product can enter the ideal only through at least one factor, a condition equivalent in commutative rings to domain-valued quotient.
The target is a member or subtype of the broader source class.
milne-algebraic-number-theorystacks-algebra-textThis is an authored directed relation from the source endpoint to the target endpoint.
The ideal determines the equivalence relation used in , and ideal absorption is what makes multiplication of cosets independent of representative.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
stacks-algebra-text