Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584937 | Journal of Algebra | 2014 | 39 Pages |
Abstract
We present a general solution of the isomorphism and multiplicity problems, restricted to the class of all modules lying in homogeneous tubes, for tame algebras (Theorem 2.4). We introduce a notion of the characteristic polynomial of a module, which plays an analogous role as in the classical situation. This notion uses a Smith form Δ(HB(M))Δ(HB(M)) of certain polynomial matrix HB(M)HB(M) associated to a module M and a bimodule B parametrizing a family of homogeneous modules FF. We show that Δ(HB(M))Δ(HB(M)) encodes an essential information on a decomposition of M into a direct sum of indecomposables from FF ( Theorem 2.2 and Theorem 2.3).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Piotr Dowbor, Andrzej Mróz,