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Greg Oman
Greg Oman
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Here is my question:

Let $R$ beDoes there exist an infinite commutative ring $R$ with identity. Does there exist with an indecomposable injective (unitary) $R$-module $M$ of larger cardinality than $R$ with the additional property that $M$ has a minimum submodule (that is, a nonzero $R$-submodule $N$ such that $N\leq K$ for every nonzero $R$-submodule $K$ of $M$)? This question is equivalent to the question obtained by dropping the adjective "indecomposable injective."

This is a bit out of my research area, but I would really like to know the answer for a paper I'm working on. Any references would be much appreciated.

Thanks!

Here is my question:

Let $R$ be an infinite commutative ring with identity. Does there exist an indecomposable injective (unitary) $R$-module $M$ of larger cardinality than $R$ with the additional property that $M$ has a minimum submodule (that is, a nonzero $R$-submodule $N$ such that $N\leq K$ for every nonzero $R$-submodule $K$ of $M$)? This question is equivalent to the question obtained by dropping the adjective "indecomposable injective."

This is a bit out of my research area, but I would really like to know the answer for a paper I'm working on. Any references would be much appreciated.

Thanks!

Here is my question:

Does there exist an infinite commutative ring $R$ with identity with an indecomposable injective (unitary) $R$-module $M$ of larger cardinality than $R$ with the additional property that $M$ has a minimum submodule (that is, a nonzero $R$-submodule $N$ such that $N\leq K$ for every nonzero $R$-submodule $K$ of $M$)? This question is equivalent to the question obtained by dropping the adjective "indecomposable injective."

This is a bit out of my research area, but I would really like to know the answer for a paper I'm working on. Any references would be much appreciated.

Thanks!

Source Link
Greg Oman
Greg Oman
  • 131
  • 1
  • 5

A question about "large" indecomposable injectives over commutative rings

Here is my question:

Let $R$ be an infinite commutative ring with identity. Does there exist an indecomposable injective (unitary) $R$-module $M$ of larger cardinality than $R$ with the additional property that $M$ has a minimum submodule (that is, a nonzero $R$-submodule $N$ such that $N\leq K$ for every nonzero $R$-submodule $K$ of $M$)? This question is equivalent to the question obtained by dropping the adjective "indecomposable injective."

This is a bit out of my research area, but I would really like to know the answer for a paper I'm working on. Any references would be much appreciated.

Thanks!