FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 2, PAGES 101-113

**Construction of the syzygy module in automaton monomial algebras**

S.
A.
Ilyasov

Abstract

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In this paper, we consider the problem of algorithmically
constructing the left syzygy module for a finite system of
elements in an automaton monomial algebra.
The class of automaton monomial algebras includes free associative
algebras and finitely presented algebras.
In such algebras the left syzygy module for a finite system of
elements is finitely generated.
In general, the left syzygy module in an automaton monomial algebra is
not finitely generated.
Nevertheless, the generators of the left syzygy module have
a recursive specification with the help of regular sets.
This allows one to solve many algorithmic problems in automaton
monomial algebras.
For example, one can solve linear equations, recognize the membership
in a left ideal, and recognize zero-divisors.

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Last modified: June 9, 2005