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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An improved upper bound for global dimension of semigroup algebras


Author: William R. Nico
Journal: Proc. Amer. Math. Soc. 35 (1972), 34-36
MSC: Primary 20M25; Secondary 16A60
DOI: https://doi.org/10.1090/S0002-9939-1972-0296182-8
MathSciNet review: 0296182
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Abstract: An upper bound for the global dimension of the semigroup algebra of a finite regular monoid in terms of an ideal series for the monoid is determined by the partially ordered set of $ \mathcal{I}$-classes of the monoid. In particular, if the monoid is combinatorial, the global dimension of the algebra is bounded by the sum of the global dimension of the coefficient ring and twice the length of the longest chain of $ \mathcal{I}$-classes in the monoid.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0296182-8
Keywords: Homological dimension, semigroup, semigroup algebra, rings
Article copyright: © Copyright 1972 American Mathematical Society