An improved upper bound for global dimension of semigroup algebras
William R. Nico · Proceedings of the American Mathematical Society · 1972
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 I \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 I \mathcal {I} -classes in the monoid.