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Castelnuovo-Mumford regularity of products of ideals.

Aldo Conca, Jürgen Herzog (2003)

Collectanea Mathematica

The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask,...

Composition-diamond lemma for modules

Yuqun Chen, Yongshan Chen, Chanyan Zhong (2010)

Czechoslovak Mathematical Journal

We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra s l 2 , the Verma module over a Kac-Moody algebra, the Verma module...

Construction of a controller with a generalized linear immersion

Javier Diaz-Vargas, Dennis Tuyub-Puc, Celia Villanueva-Novelo (2011)

Kybernetika

Gröbner bases for modules are used to calculate a generalized linear immersion for a plant whose solutions to its regulation equations are polynomials or pseudo-polynomials. After calculating the generalized linear immersion, we build the controller which gives the robust regulation.

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