We generalize the notions of n-cluster tilting subcategories and τ-selfinjective algebras into
n-precluster tilting subcategories and τ n-selfinjective algebras, where we show that a …

Tachikawa's second conjecture predicts that a finitely generated, orthogonal module over a
finite-dimensional self-injective algebra is projective. This conjecture is an important part of …

We study certain special tilting and cotilting modules for an algebra with positive dominant
dimension, each of which is generated or cogenerated (and usually both) by projective …

We prove that a finite dimensional algebra $ A $ with representation-finite subcategory
consisting of modules that are semi-Gorenstein-projective and $ n $-th syzygy modules is …

Rigidity dimension of algebras is a new homological dimension which measures the quality
of resolutions of algebras by algebras of finite global dimension and large dominant …

We introduce the class of dominant Auslander-Gorenstein algebras as a generalisation of
higher Auslander algebras and minimal Auslander-Gorenstein algebras, and give their …

The rigidity degree of a generator-cogenerator determines the dominant dimension of its
endomorphism algebra, and is closely related to a recently introduced homological …

Gendo-symmetric algebras were introduced by Fang and Koenig (Trans. Amer. Math. Soc.,
7: 5037–5055, 2016) as a generalisation of symmetric algebras. Namely, they are …

We give new properties of algebras with finite self-injective dimension coinciding with the
dominant dimension d≥ 2, which are called minimal Auslander–Gorenstein algebras in the …

We give new improved bounds for the dominant dimension of Nakayama algebras and use
those bounds to give a classification of Nakayama algebras with n simple modules that are …