… of example, that modules of Krull dimension 0 are precisely nonzero artinian modules; and
that K … to our point of view in regarding modules with Krull dimension as generalizing artinian …

… semisimple modules as well as, all Artinian modules with a … modules with classical Krull
dimension zero. For a multiplication module over a commutative ring, the notion of classical Krull …

… -dimension to give a generalization of Krull 's Principal Ideal Theorem. In Section 111 we look
at artinian modules and dualize the noetherian module … say that M has Krull dimension if L(…

… module M with Krull dimension. Since every Artinian (Noetherian) R-module has Krull
dimension, we infer that Artinian modules coincide with Noetherian modules over the rings that we …

… length and the Noetherian-dimension of an Artinian module and as a consequence we find
… set of an Artinian module over any ring in terms of its Noetherian-dimension. In particular, this …

… is Artinian if and only if every small submodule of it is Artinian… A has Krull dimension, does
Rad(A) have Krull dimension? … of A has Krull dimension, does A have Krull dimension? By an …

… is an α-Krull module then the Krull dimension of M is … Artinian module M has Krull dimension
and k-dim M ≤ α. Consequently, if M is an almost Artinian module, then either M is Artinian …

… a semi-prime ring with Krull dimension is a Goldie ring and we … Krull dimension is less than
or equal to Krull dimension. This … Krull dimension has a semi-simple artin vight ~otient ring. …

… modules with this dimension. In particular, we show that an R-module M has Krull dimension
… We show that any p-Artinian module M contains a parallel submodule which is a direct sum …

… The next result is the key for obtaining an embedding of a -torsionfree ring R with right Krull
dimension into a right artinian ring, because it describes the set of regular elements of R in …