Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1026.13003
Alexeev, Dmitri
On quasi-projective uniserial modules. (English)
[J] Rend. Semin. Mat. Univ. Padova 105, 65-76 (2001). ISSN 0041-8994

The author studies quasi-projective uniserial modules over a valuation domain $R$ and, in particular, quasi-projective ideals of $R$. The quasi-projectivity of a uniserial $R$-module $U$ is characterized in terms of lifting of endomorphisms of factors of $U$ and this characterization is used to describe quasi-projective ideals of $R$ in terms of the completeness of certain localizations of factor rings of $R$. In the case of archimedean ideals this description becomes more explicit and it is shown that, if the maximal ideal $P$ of $R$ is infinitely generated, a non-principal archimedean ideal $I$ is quasi-projective if and only if $R/K$ is complete in the $R/K$-topology for each archimedean ideal $K\not\cong P$ (and, in this case, all archimedean ideals of $R$ are quasi-projective).
[José L.Gomez-Pardo (Santiago de Compostela)]

MSC 2000:: *13C10 Projective modules, etc.
13F30 Valuation rings
13J20 Global topological rings

Keywords: quasi-projective module; uniserial module; valuation domain; archimedean ideal

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]