Upper bounds for the dominant dimension of Nakayama and related algebras

TL;DR

This paper establishes optimal upper bounds for the dominant dimensions of Nakayama and related algebras, resolving open questions and confirming conjectures in the field.

Contribution

It provides the first sharp bounds for dominant dimensions in Nakayama and certain related algebras, addressing open problems and conjectures.

Findings

Optimal upper bounds for dominant dimensions of Nakayama algebras.

Resolution of a question posed by Abrar.

Proof of Yamagata's conjecture for monomial algebras.

Abstract

Optimal upper bounds are provided for the dominant dimensions of Nakayama algebras and more generally algebras $A$ with an idempotent $e$ such that there is a minimal faithful injective-projective module $eA$ and such that $eAe$ is a Nakayama algebra. This answers a question of Abrar and proves a conjecture of Yamagata for monomial algebras.