Abstract
The goal of this paper is to investigate whether the Ext-groups of all pairs (M, N) of modules over Nakayama algebras of type (n,n,n) satisfy the condition ExtΛn(M,N)=0 for n >> 0 ? ExtΛn(M,N)=0 for n >> 0. We achieve that by discussing the Ext-groups of Nakayama algebra with projectives of lengths 3n+1 and 3n+2 using combinations of modules of different lengths.
Highlights
IntroductionWe describe homological properties of Nakayama algebras
In this paper, we describe homological properties of Nakayama algebras
The main contribution of this paper is to investigate whether the Ext-groups of all pairs (M, N ) of modules over Nakayama algebras of type (n, n, n) satisfy the condition ExtΛn (M, N ) = 0 for n 0 ⇔ ExtΛn ( N, M ) = 0 for n 0
Summary
We describe homological properties of Nakayama algebras. The algebra Ʌ is a Nakayama algebra if every projective indecomposable and every injective indecomposable Ʌ-module is uniserial. In other words, these modules have a unique composition series, (see Schröer [1]). Nakayama algebras are finite dimensional and representation-finite algebras that have a nice representation theory in the sense that the finite-dimensional indecomposable modules are easy to describe. The main contribution of this paper is to investigate whether the Ext-groups of all pairs (M , N ) of modules over Nakayama algebras of type (n, n, n) satisfy the condition ExtΛn (M , N ) = 0 for n 0 ⇔ ExtΛn ( N, M ) = 0 for n 0
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