caa a22 4500 445345071 CHVBK 20180317142826.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00233-010-9264-8 doi (NATIONALLICENCE)springer-10.1007/s00233-010-9264-8 Husainov Ahmet Komsomolsk-on-Amur State Technical University, Lenina prosp, 27, Komsomolsk-on-Amur, Russian Federation aut The global dimension of a trace monoid ring [Elektronische Daten] [Ahmet Husainov] The article is devoted to the global dimension of a R-monoid ring RM(E,I) of a free partially commutative monoid. We prove that if the supremum of numbers of distinct pairwise commuting elements in E is equal to n, then gl dim RM(E,I)=n+gl dim R. Moreover, we get a generalized formula for the global dimensions of the categories of M(E,I)-objects in Abelian categories. Springer Science+Business Media, LLC, 2010 Cohomology of small categories nationallicence Free partially commutative monoid nationallicence Polynomial ring nationallicence Partially commuting variables nationallicence Semigroup Forum Springer-Verlag 82/2(2011-04-01), 261-270 0037-1912 82:2<261 2011 82 233 https://doi.org/10.1007/s00233-010-9264-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-010-9264-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Husainov Ahmet Komsomolsk-on-Amur State Technical University, Lenina prosp, 27, Komsomolsk-on-Amur, Russian Federation aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 82/2(2011-04-01), 261-270 0037-1912 82:2<261 2011 82 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer