The multiplicity problem for indecomposable decompositions of modules over a finite-dimensional algebra. Algorithms and a computer algebra approach
P Dowbor, A Mróz - Colloquium Mathematicum, 2007 - infona.pl
P Dowbor, A Mróz
Colloquium Mathematicum, 2007•infona.plGiven a module M over an algebra Λ and a complete set 𝓧 of pairwise nonisomorphic
indecomposable Λ-modules, the problem of determining the vector $ m (M)=(m_X) _ {X∈
𝓧}∈ ℕ^{𝓧} $ such that $ M≅⨁ _ {X∈ 𝓧} X^{m_X} $ is studied. A general method of finding
the vectors m (M) is presented (Corollary 2.1, Theorem 2.2 and Corollary 2.3). It is discussed
and applied in practice for two classes of algebras: string algebras of finite representation
type and hereditary algebras of type $ 𝔸̃_ {p, q} $. In the second case detailed algorithms …
indecomposable Λ-modules, the problem of determining the vector $ m (M)=(m_X) _ {X∈
𝓧}∈ ℕ^{𝓧} $ such that $ M≅⨁ _ {X∈ 𝓧} X^{m_X} $ is studied. A general method of finding
the vectors m (M) is presented (Corollary 2.1, Theorem 2.2 and Corollary 2.3). It is discussed
and applied in practice for two classes of algebras: string algebras of finite representation
type and hereditary algebras of type $ 𝔸̃_ {p, q} $. In the second case detailed algorithms …
Given a module M over an algebra Λ and a complete set 𝓧 of pairwise nonisomorphic indecomposable Λ-modules, the problem of determining the vector such that is studied. A general method of finding the vectors m(M) is presented (Corollary 2.1, Theorem 2.2 and Corollary 2.3). It is discussed and applied in practice for two classes of algebras: string algebras of finite representation type and hereditary algebras of type $𝔸̃_{p,q}$. In the second case detailed algorithms are given (Algorithms 4.5 and 5.5).
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