On the isomorphism problem for finite-dimensional binomial algebras

ABSTRACT

Binomial algebras are finitely presented algebras defined by monomials or binomials. Given two binomial algebras, one important problem is to decide whether or not they are isomorphic as algebras. We study an algorithm for solving this problem, when both algebras are finite-dimensional over a field. In particular, when they are monomial algebras (i.e. binomial algebras defined by monomials only), the problem has already been completely solved by the presentation uniqueness. In this paper, we provide some necessary conditions in terms of partially ordered sets for two certain binomial algebras to be isomorphic. In other words, invariants of the binomial algebras are presented. These conditions together serve as an effective procedure for solving the isomorphism problem.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Algebraic algorithms

General Terms:
Algorithms, Theory