An improved upper bound for global dimension of semigroup algebras
William R. Nico
Proc. Amer. Math. Soc. 35 (1972), 34-36
Primary 20M25; Secondary 16A60
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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 -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 -classes in the monoid.
Algebraic theory of machines, languages, and semigroups, Edited
by Michael A. Arbib. With a major contribution by Kenneth Krohn and John L.
Rhodes, Academic Press, New York-London, 1968. MR 0232875
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B. Preston, The algebraic theory of semigroups. Vol. I,
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R. Nico, Homological dimension in semigroup algebras, J.
Algebra 18 (1971), 404–413. MR 0277626
- M. A. Arbib (Editor) Algebraic theory of machines, languages, and semigroups, Academic Press, New York, 1968. MR 38 #1198. MR 0232875 (38:1198)
- A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. 1, Math. Surveys, no. 7, Amer. Math. Soc., Providence, R.I., 1961. MR 24 #A2627. MR 0132791 (24:A2627)
- W. Nico, Homological dimension in semigroup algebras, J. Algebra 18 (1971), 404-413. MR 43 #3359. MR 0277626 (43:3359)
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