EuDML | Browse

Let $R$ be a commutative Noetherian ring and $𝔞$ an ideal of $R$ . We introduce the concept of $𝔞$ -weakly Laskerian $R$ -modules, and we show that if $M$ is an $𝔞$ -weakly Laskerian $R$ -module and $s$ is a non-negative integer such that ${Ext}_{R}^{j} (R / 𝔞, H_{𝔞}^{i} (M))$ is $𝔞$ -weakly Laskerian for all $i < s$ and all $j$ , then for any $𝔞$ -weakly Laskerian submodule $X$ of $H_{𝔞}^{s} (M)$ , the $R$ -module ${Hom}_{R} (R / 𝔞, H_{𝔞}^{s} (M) / X)$ is $𝔞$ -weakly Laskerian. In particular, the set of associated primes of $H_{𝔞}^{s} (M) / X$ is finite. As a consequence, it follows that if $M$ is a finitely generated $R$ -module and $N$ is an $𝔞$ -weakly...

A generalization of Ulm subgroups

Kenneth Messa (1977)

Rendiconti del Seminario Matematico della Università di Padova

A note on basic free modules and the $S_{n}$ condition.

Marcelo, Agustín, Marcelo, Félix, Rodríguez, César (2006)

Portugaliae Mathematica. Nova Série

A Note on Derivations of Commutative Rings.

Surender K. Gupta (1974)

Mathematische Zeitschrift

A note on generalized primary rings

R. Chaudhuri (1976)

Matematički Vesnik

A note on indecomposable modules over valuation domains

Matt D. Lunsford (1995)

Rendiconti del Seminario Matematico della Università di Padova

A note on indecomposable projective modules

A. G. Naoum (1989)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

A Note on Projective Modules Over Polynomial Rings.

S.M. Bhatwadekar (1987)

Mathematische Zeitschrift

A remark on projectively closed purities

Ladislav Bican (1974)

Czechoslovak Mathematical Journal

A simple proof of uniqueness for torsion modules over principal ideal domains.

J. L. García Roig (1985)

Stochastica

The aim of this note is to give an alternative proof of uniqueness for the decomposition of a finitely generated torsion module over a P.I.D. (= principal ideal domain) as a direct sum of indecomposable submodules.Our proof tries to mimic as far as we can the standard procedures used when dealing with vector spaces.For the sake of completeness we also include a proof of the existence theorem.

Algèbres localement polynomiales

Thierry Levasseur (1976/1977)

Groupe d'étude d'algèbre Groupe d'étude d'algèbre

Almost Artinian modules.

James Hein (1979)

Mathematica Scandinavica

Almost free splitters

Rüdiger Göbel, Saharon Shelah (1999)

Colloquium Mathematicae

Let R be a subring of the rationals. We want to investigate self splitting R-modules G, that is, such that $E x t_{R} (G, G) = 0$ . For simplicity we will call such modules splitters (see [10]). Also other names like stones are used (see a dictionary in Ringel’s paper [8]). Our investigation continues [5]. In [5] we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In [5] we concentrated on splitters which are larger...

An addendum and corrigendum to "Almost free splitters" (Colloq. Math. 81 (1999), 193-221)

Rüdiger Göbel, Saharon Shelah (2001)

Colloquium Mathematicae

Let R be a subring of the rational numbers ℚ. We recall from [3] that an R-module G is a splitter if $E x t ¹_{R} (G, G) = 0$ . In this note we correct the statement of Main Theorem 1.5 in [3] and discuss the existence of non-free splitters of cardinality ℵ₁ under the negation of the special continuum hypothesis CH.

An algebraic framework for linear identification

Michel Fliess, Hebertt Sira-Ramírez (2003)

ESAIM: Control, Optimisation and Calculus of Variations

A closed loop parametrical identification procedure for continuous-time constant linear systems is introduced. This approach which exhibits good robustness properties with respect to a large variety of additive perturbations is based on the following mathematical tools: (1) module theory; (2) differential algebra; (3) operational calculus. Several concrete case-studies with computer simulations demonstrate the efficiency of our on-line identification scheme.

Currently displaying 1 – 20 of 160

Page 1 Next