We investigate several homological aspects of recollements of abelian categories. In
particular, we study how various homological invariants and dimensions of the categories …

Abstract Let $ A $ and $ B $ be rings, $ U $ a $(B, A) $-bimodule, and $ T=\left (\begin
{smallmatrix} A & 0\\U & B\\\end {smallmatrix}\right) $ the triangular matrix ring. In this paper …

Path algebras from quivers are a fundamental class of algebras with wide applications. Yet it
is challenging to describe their universal properties since their underlying path semigroups …

A recent result of Araya asserts that if the Auslander–Reiten conjecture holds in
codimension one for a commutative Gorenstein ring R, then it holds for R. This note extends …

HEREDITARY AND SEMIHEREDITARY REPRESENTATIONS OF QUIVERS 1. Introduction In
this paper, we are interested in hereditary and semi Page 1 Bull. Korean Math. Soc. 58 (2021) …

In this note, it is shown that the validity of the Auslander–Reiten conjecture for a given d-
dimensional Cohen–Macaulay local ring R depends on its validity for all direct summands of …

Let (R, m) be ad-dimensional commutative Noetherian local ring. Let M denote the
morphism category of finitely generated R-modules, and let S be the full subcategory of M …

Περίληψη Σε αυτήν τη διδακτορική διατριβή ελετά ε ο ολογικές διαστάσεις που ε φανίζονται
στη Θεωρία Αναπαραστάσεων Αλγεβρών του Artin. Η βασική ας έρευνα επικεντρώνεται στη …