Bounds on Frobenius dimension

D. Artenstein; J. Cóppola; J. Finot; A. González; G. Mata

Bounds on Frobenius dimension

Rings and Algebras 2026-07-17 v1

Authors: D. Artenstein , J. Cóppola , J. Finot , A. González , G. Mata

Abstract

In this article, we prove two types of results about the Frobenius dimension of associative algebras. First, we refine the known upper bound for the Frobenius dimension of a finite dimensional algebra in terms of its dimension as a vector space, and show that the only algebras reaching this bound are radical square zero algebras associated with single-vertex quivers. Second, we compute Frobenius dimension for low-dimensional algebras explicitly, and for truncated path algebras in terms of paths with no detours in their underlying quivers.

Cite

@article{arxiv.2607.15999,
  title  = {Bounds on Frobenius dimension},
  author = {D. Artenstein and J. Cóppola and J. Finot and A. González and G. Mata},
  journal= {arXiv preprint arXiv:2607.15999},
  year   = {2026}
}