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2 votes
Accepted

The Prüfer group $\mathbb{Z}(p^{\infty})$ as a $\mathbb{Z}$ module is not projective.

A projective module over an integral domain is torsion-free, so a nonzero module in which every element is torsion is about the worst thing you could even imagine might be projective. Your proof is ...
KCd's user avatar
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2 votes

Examples of uniserial rings which are non self-injective.

A self injective domain has to be a field, so any commuative valuation ring will do as long as it is not a field. For example: $F[[x]]$ for a field $F$ $\mathbb Z_p$ $\mathbb Z_{(p)}$
rschwieb's user avatar
  • 155k
1 vote
Accepted

Giving examples of matrix rings with just one or a few maximal ideals and with easy lattices to compute.

It looks like by "matrix ring" you just mean "ring with elements that are matrices" rather than something of the form $M_n(R)$. The ideals of $M_n(R)$ are all completely ...
rschwieb's user avatar
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