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2008 On the Leech dimension of a free partially commutative monoid
Ahmet A. Husainov
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Tbilisi Math. J. 1: 71-87 (2008). DOI: 10.32513/tbilisi/1528768824


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 $\leqslant n$. 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.


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Ahmet A. Husainov. "On the Leech dimension of a free partially commutative monoid." Tbilisi Math. J. 1 71 - 87, 2008.


Received: 6 September 2007; Revised: 13 April 2008; Accepted: 16 May 2008; Published: 2008
First available in Project Euclid: 12 June 2018

zbMATH: 1160.18005
MathSciNet: MR2480122
Digital Object Identifier: 10.32513/tbilisi/1528768824

Primary: 18G20
Secondary: 18A25, 18E25, 18G10, 20M25, 68Q25

Rights: Copyright © 2008 Tbilisi Centre for Mathematical Sciences


Vol.1 • 2008
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