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Complexity and periodicity

Petter Andreas Bergh (2006)

Colloquium Mathematicae

Let M be a finitely generated module over an Artin algebra. By considering the lengths of the modules in the minimal projective resolution of M, we obtain the Betti sequence of M. This sequence must be bounded if M is eventually periodic, but the converse fails to hold in general. We give conditions under which it holds, using techniques from Hochschild cohomology. We also provide a result which under certain conditions guarantees the existence of periodic modules. Finally, we study the case when...

Component clusters for acyclic quivers

Sarah Scherotzke (2016)

Colloquium Mathematicae

The theory of Caldero-Chapoton algebras of Cerulli Irelli, Labardini-Fragoso and Schröer (2015) leads to a refinement of the notions of cluster variables and clusters, via so-called component clusters. We compare component clusters to classical clusters for the cluster algebra of an acyclic quiver. We propose a definition of mutation between component clusters and determine the mutation relations of component clusters for affine quivers. In the case of a wild quiver, we provide bounds for the size...

Componentwise injective models of functors to DGAs

Marek Golasiński (1997)

Colloquium Mathematicae

The aim of this paper is to present a starting point for proving existence of injective minimal models (cf. [8]) for some systems of complete differential graded algebras.

Composition of preradicals

Ladislav Bican, Pavel Jambor, Tomáš Kepka, Petr Němec (1974)

Commentationes Mathematicae Universitatis Carolinae

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...

Compositions on the ring of polynomials in two indeterminates.

Veldsman, Stefan (2006)

Mathematica Pannonica

Computation of the mapping of factorization by the radical for $K_{0}^{+}$ of the endomorphism ring.

Lebedinskii, D.M. (1999)

Zapiski Nauchnykh Seminarov POMI

Computational techniques for PI-algebras

V. Drensky (1990)

Banach Center Publications

Computing homomorphism spaces between modules over finite dimensional algebras.

Lux, Klaus M., Szőke, Magdolna (2003)

Experimental Mathematics

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.