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Mat. Sb., 2008, Volume 199, Number 12, Pages 129–154 (Mi msb6357)  

This article is cited in 7 scientific papers (total in 7 papers)

Cubical homology and the Leech dimension of free partially commutative monoids

A. A. Khusainov

Komsomolsk-on-Amur State Technical University

Abstract: The paper is devoted to problems arising when applying homological algebra to computer science. It is proved that the Leech dimension of a free partially commutative monoid is equal to the least upper bound of the cardinalities of finite subsets of pairwise commuting generators of the monoid. For an arbitrary free partially commutative monoid $M(E,I)$ in which every subset of pairwise commuting generators is finite and for any contravariant natural system $F$ on $M(E,I)$ we construct a semicubical set $T(E,I)$ with a homological system $\overline F$ on this set such that the Leech homology groups $H_n(M(E,I),F)$ are isomorphic to the cubical homology groups $H_n(T(E,I),\overline F)$. Complexes of Abelian groups are also constructed enabling one to obtain (under additional finiteness conditions) algorithms for computing the Leech homology groups and homology groups with coefficients in right $M(E,I)$-modules.
Bibliography: 16 titles.

DOI: https://doi.org/10.4213/sm6357

Full text: PDF file (658 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2008, 199:12, 1859–1884

Bibliographic databases:

UDC: 512.66
MSC: Primary 18G20, 20J05; Secondary 55U35, 68Q85
Received: 28.04.2008

Citation: A. A. Khusainov, “Cubical homology and the Leech dimension of free partially commutative monoids”, Mat. Sb., 199:12 (2008), 129–154; Sb. Math., 199:12 (2008), 1859–1884

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Husainov A.A., “The global dimension of a trace monoid ring”, Semigroup Forum, 82:2 (2011), 261–270  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. A. Khusainov, “Gruppy gomologii asinkhronnykh sistem, setei Petri i yazykov trass”, Sib. elektron. matem. izv., 9 (2012), 13–44  mathnet
    3. A. A. Khusainov, “The cubical homology of trace monoids”, Dalnevost. matem. zhurn., 12:1 (2012), 108–122  mathnet
    4. A. A. Khusainov, “The global dimension of polynomial categories in partially commuting variables”, Siberian Math. J., 53:4 (2012), 757–762  mathnet  crossref  mathscinet  isi
    5. Husainov A.A., “The homology of partial monoid actions and Petri nets”, Appl. Categor. Struct., 21:6 (2013), 587–615  crossref  mathscinet  zmath  isi  elib  scopus
    6. Calvo-Cervera M., Cegarra A.M., “(Co)homology of cyclic monoids”, Int. J. Algebr. Comput., 26:5 (2016), 887–910  crossref  mathscinet  zmath  isi  scopus
    7. Husainov A.A., “Homology Groups of Cubical Sets”, Appl. Categ. Struct., 27:2 (2019), 199–216  crossref  mathscinet  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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