In this paper, we investigate the relative dominant dimension with respect to an injective
module and characterize the algebras with finite relative dominant dimension. As an …

In this paper, we prove a higher dimensional version of Auslander-Iyama-Solberg
correspondence. Iyama and Solberg have shown a bijection between $ n $-minimal …

Homological algebra is extensively used in the representation theory of artin algebras and
elsewhere. Relative homological algebra has played a much less prominent role. The aim of …

Over a finite-dimensional algebra A, simple A-modules that have projective dimension one
have special properties. For example, Geigle-Lenzing studied them in connection to …

We consider maximal non-l-intertwining collections, which are a higher-dimensional version
of the maximal non-crossing collections which give clusters of Plücker coordinates in the …

Rigidity dimension is a new homological dimension which is intended to measure the quality
of the best resolution of an algebra. In this paper, we determine the rigidity dimensions of …

Given an algebra with an idempotent, we introduce two procedures to construct families of
new algebras, termed mirror-reflective algebras and reduced mirror-reflective algebras. We …

Recently, Chen and Koenig in\cite {CheKoe} and Iyama and Solberg in\cite {IyaSol}
independently introduced and characterised algebras with dominant dimension coinciding …

The famous Nakayama conjecture states that the dominant dimension of a non-selfinjective
finite dimensional algebra is finite. Yamagata (Frobenius algebras handbook of algebra, vol …

Cluster categories, introduced by Buan–Marsh–Reineke–Reiten–Todorov [BMR+ 06] and
later generalised by Amiot [Ami09], are certain 2-Calabi–Yau triangulated categories that …