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An algebraic framework for linear identification

Michel Fliess, Hebertt Sira–Ramírez (2010)

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.

CF-modules over commutative rings

Ahmed Najim, Mohammed Elhassani Charkani (2018)

Commentationes Mathematicae Universitatis Carolinae

Let R be a commutative ring with unit. We give some criterions for determining when a direct sum of two CF-modules over R is a CF-module. When R is local, we characterize the CF-modules over R whose tensor product is a CF-module.

Cominimaxness of local cohomology modules

Moharram Aghapournahr (2019)

Czechoslovak Mathematical Journal

Let R be a commutative Noetherian ring, I an ideal of R . Let t ∈ ℕ 0 be an integer and M an R -module such that Ext R i ( R / I , M ) is minimax for all i ≤ t + 1 . We prove that if H I i ( M ) is FD ≤ 1 (or weakly Laskerian) for all i < t , then the R -modules H I i ( M ) are I -cominimax for all i < t and Ext R i ( R / I , H I t ( M ) ) is minimax for i = 0 , 1 . Let N be a finitely generated R -module. We prove that Ext R j ( N , H I i ( M ) ) and Tor j R ( N , H I i ( M ) ) are I -cominimax for all i and j whenever M is minimax and H I i ( M ) is FD ≤ 1 (or weakly Laskerian) for all i .

Comultiplication modules over a pullback of Dedekind domains

Reza Ebrahimi Atani, Shahabaddin Ebrahimi Atani (2009)

Czechoslovak Mathematical Journal

First, we give complete description of the comultiplication modules over a Dedekind domain. Second, if R is the pullback of two local Dedekind domains, then we classify all indecomposable comultiplication R -modules and establish a connection between the comultiplication modules and the pure-injective modules over such domains.

Decomposition of finitely generated modules using Fitting ideals

Somayeh Hadjirezaei, Sina Hedayat (2020)

Czechoslovak Mathematical Journal

Let R be a commutative Noetherian ring and M be a finitely generated R -module. The main result of this paper is to characterize modules whose first nonzero Fitting ideal is a product of maximal ideals of R , in some cases.

Dichte Ringe*

Günther Haugner, Wolfgang Zimmermann (1974)

Mathematische Annalen

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