## On the Leech dimension of a free partially commutative monoid## Ahmet A. Husainov
We prove that the Leech dimension of any free partially commutative monoid is equal to the supremum of numbers
of its mutually commuting generators. As a consequence, we confirm a conjecture that if a free partially
commutative monoid does not contain more than n mutually commuting generators, then it is of homological
dimension
≤ n. We apply this result to the homological dimension of asynchronous
transition systems.
We positively answer the question whether the homological dimension of
an asynchronous transition system is not greater
than the maximal number of its mutually independent events.
Tbilisi Mathematical Journal, Vol. 1(2008), pp. 71-87 |