2 9 Ju n 20 06 Resolutions of free partially commutative monoids
نویسنده
چکیده
In this paper we construct a free resolution for a free partially commutative monoid and with its help prove the Husainov’s Conjecture. We follow the ideas of D. Cohen who built in [3] a resolution for the so-called graph product of groups, given resolutions for factors. The presentation of the graph product with the help of direct and free amalgamated products played the leading role at that. However the additional difficulties appear while using this method for monoids. Section 1 is devoted to basic definitions and facts concerned with free partially commutative monoids and free amalgamated products. In Section 2 the desired resolution is constructed. If the opposite is not specified all considered modules are right.
منابع مشابه
Partially Commutative Inverse Monoids
Free partially commutative inverse monoids are investigated. Analogously to free partially commutative monoids (trace monoids), free partially commutative inverse monoids are the quotients of free inverse monoids modulo a partially defined commutation relation on the generators. A quasi linear time algorithm for the word problem is presented, more precisely, we give an O(n log(n)) algorithm for...
متن کاملEfficient Solution to Some Problems in Free Partially Commutative Monoids
In theoretical computer science, and, in particular, in automata and formal language theory, questions arise concerning words and sets of words in free monoids. Results and techniques from the study of the combinatorial algebra of the free monoid have provided an “algebraic” basis for dealing with many of these questions. In recent years there has been increasing interest in properties of words...
متن کاملTransitive factorizations of free partially commutative monoids and Lie algebras
Let M(A, θ) be a free partially commutative monoid. We give here a necessary and sufficient condition on a subalphabet B ⊂ A such that the right factor of a bisection M(A, θ) = M(B, θB).T be also partially commutative free. This extends strictly the (classical) elimination theory on partial commutations and allows to construct new factorizations of M(A, θ) and associated bases of LK(A, θ).
متن کاملar X iv : m at h / 05 06 07 2 v 2 [ m at h . G R ] 1 6 Fe b 20 07 Centraliser Dimension of Partially Commutative Groups ∗ † Andrew
In paper [7] we investigated the centraliser dimension of groups. In the current paper we study properties of centraliser dimension for the class of free partially commutative groups and, as a corollary, we obtain an efficient algorithm for computation of centraliser dimension in these groups.
متن کاملSolutions of Word Equations Over Partially Commutative Structures
We give NSPACE(n logn) algorithms solving the following decision problems.Satisfiability: Is the given equation over a free partially commutative monoid with involution(resp. a free partially commutative group) solvable? Finiteness: Are there only finitely manysolutions of such an equation? PSPACE algorithms with worse complexities for the first problemare known, but so far, a P...
متن کامل