Facebook Instagram Twitter RSS Feed PodBean Back to top on side

Relative purity over Noetherian rings

In: Mathematica Slovaca, vol. 57, no. 4
Ladislav Bican
Detaily:
Rok, strany: 2007, 333 - 338
O článku:
In this note we are going to show that if $M$ is a left module over a left noetherian ring $R$ of the infinite cardinality $λ≥ |R|$, then its injective hull $E(M)$ is of the same size. Further, if $M$ is an injective module with $|M|≥ (2λ)+$ and $K≤ M$ is its submodule such that $|M/K|≤λ$, then $K$ contains an injective submodule $L$ with $|M/L|≤ 2λ$. These results are applied to modules which are torsionfree with respect to a given hereditary torsion theory and generalize the results obtained by different methods in author's previous papers: [\textit{A note on pure subgroups}, Contributions to General Algebra 12. Proceedings of the Vienna Conference, June 3–6, 1999, Verlag Johannes Heyn, Klagenfurt, 2000, \mbox{pp. 105–107}], [\textit{Pure subgroups}, Math. Bohem. \textbf{126} (2001), 649–652].
Ako citovať:
ISO 690:
Bican, L. 2007. Relative purity over Noetherian rings. In Mathematica Slovaca, vol. 57, no.4, pp. 333-338. 0139-9918.

APA:
Bican, L. (2007). Relative purity over Noetherian rings. Mathematica Slovaca, 57(4), 333-338. 0139-9918.