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On the structure of linear recurrent error-control codes

Michel Fliess (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.

On the structure of linear recurrent error-control codes

Michel Fliess (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. We are also proposing a new connection between fixed convolutional codes and linear block codes. These results are obtained thanks to a module-theoretic framework which has been previously developed for linear control.

On the structure of sequentially Cohen-Macaulay bigraded modules

Leila Parsaei Majd, Ahad Rahimi (2015)

Czechoslovak Mathematical Journal

Let K be a field and S = K [ x 1 , ... , x m , y 1 , ... , y n ] be the standard bigraded polynomial ring over K . In this paper, we explicitly describe the structure of finitely generated bigraded “sequentially Cohen-Macaulay” S -modules with respect to Q = ( y 1 , ... , y n ) . Next, we give a characterization of sequentially Cohen-Macaulay modules with respect to Q in terms of local cohomology modules. Cohen-Macaulay modules that are sequentially Cohen-Macaulay with respect to Q are considered.

On the symmetric algebra of certain first syzygy modules

Gaetana Restuccia, Zhongming Tang, Rosanna Utano (2022)

Czechoslovak Mathematical Journal

Let ( R , 𝔪 ) be a standard graded K -algebra over a field K . Then R can be written as S / I , where I ( x 1 , ... , x n ) 2 is a graded ideal of a polynomial ring S = K [ x 1 , ... , x n ] . Assume that n 3 and I is a strongly stable monomial ideal. We study the symmetric algebra Sym R ( Syz 1 ( 𝔪 ) ) of the first syzygy module Syz 1 ( 𝔪 ) of 𝔪 . When the minimal generators of I are all of degree 2, the dimension of Sym R ( Syz 1 ( 𝔪 ) ) is calculated and a lower bound for its depth is obtained. Under suitable conditions, this lower bound is reached.

On torsion Gorenstein injective modules

Okyeon Yi (1998)

Archivum Mathematicum

In this paper, we define Gorenstein injective rings, Gorenstein injective modules and their envelopes. The main topic of this paper is to show that if D is a Gorenstein integral domain and M is a left D -module, then the torsion submodule t G M of Gorenstein injective envelope G M of M is also Gorenstein injective. We can also show that if M is a torsion D -module of a Gorenstein injective integral domain D , then the Gorenstein injective envelope G M of M is torsion.

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