Let R be a ring and f : M ?? N a morphism of left...

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Let R be a ring and f : M ?? N a morphism of left R-modules. Show that:
c) K := {m ? M | f(m) = 0} satisfies the Universal Property of Kernels.
d) N/f(M) satisfies the Universal Property of Cokernels.

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4.3 Ratings (686 Votes)

cSuppose that i K M the inclusionObserve that f o i x fx 0 for all x in KThus foi is the zero mapNow suppose that K is an Rmodule and g K M be a morphism such that f o g K N is the See Answer

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Let R be a ring and f : M ?? N a morphism of left...

50.1K

Verified Solution

Question

Advance Math

Let R be a ring and f : M ?? N a morphism of left R-modules. Show that:
c) K := {m ? M | f(m) = 0} satisfies the Universal Property of Kernels.
d) N/f(M) satisfies the Universal Property of Cokernels.

Answer & Explanation Solved by verified expert

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Let R be a ring and f : M ?? N a morphism of left...

50.1K

Verified Solution

Question

Advance Math

Let R be a ring and f : M ?? N a morphism of left R-modules. Show that:c) K := {m ? M | f(m) = 0} satisfies the Universal Property of Kernels.d) N/f(M) satisfies the Universal Property of Cokernels.

Answer & Explanation Solved by verified expert

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Let R be a ring and f : M ?? N a morphism of left R-modules. Show that:
c) K := {m ? M | f(m) = 0} satisfies the Universal Property of Kernels.
d) N/f(M) satisfies the Universal Property of Cokernels.