Does Hopkins' theorem extend to projective modules, ie, are projective Artinian modules
Noetherian? An example is given to answer this question in the negative; however, we show …

We prove that the Krull-Schmidt theorem fails for artinian modules. This answers a question
asked by Krull in 1932. In fact we show that if S is a module-finite algebra over a semilocal …

It is well known that a module M has finite length if and only if it is semi-artinian and
Noetherian or, equivalently, semi-noetherian and artinian. Our main result shows that finite …

Full article: Conditions for a ring to be Noetherian or Artinian Skip to Main Content Taylor
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In this note we shall use the same notations and terminologies as in [2]. In [2] we proved that,
if R is a weakly noetherian ring for which dim (mspec (R)) is finite, any nonfinitely generated …

In [7J Serre showed that, given a commutative Noetherian ring Rand a projective, finitely
generated R-module M with f-rk (M) dim (max (R))+ 1, then M M'$ R. When Bass considered …

En 1958, Kaplansky [6] inaugura l'etude des modules projectifs de type infini en montrant
qu'ils sont somme directe de modules de type denombrable, et qu'ils sont libres sur les …

Cukerman [2], Shanny [5], and Ware [7] have shown that a ring R is Artin semisimple if and
only if R has a nonfinitely generated free module with regular endomorphism ring. This …

We give a simplified proof to the following theorem due to D. Quillen: if A is a commutative
noetherian ring of global dimension $\leqslant 1$, then finitely generated projective modules …

Kaplansky proved in [3, Theorem 2] that over a local 1 ring any projective module is free.
Another large class of projective modules were shown to be free a few years later. Bass [2 …