A Classification of Finite-dimensional Monomial Algebras
Kiyoshi Shirayanagi · Birkhäuser Boston eBooks · 1991
Monomial algebras are finitely presented algebras defined by monomials. This notion is considered the most fundamental of “standard” finitely presented algebras, in the sense that they have finite non-commutative Gröbner bases as defining relations.This paper classifies and constructs finite-dimensional monomial algebras modulo an algebra isomorphism by means of trees of nonzero monomials. These trees are deeply related to partially ordered sets called LSGOP. As a corollary, it is shown that every finite-dimensional monomial algebra has a unique irredundant presentation up to a permutation of generators. This result will serve as an effective method for solving the isomorphism problem in this area.