Anderson's conjecture and the maximal monoid class over which projective modules are free

A positive solution is given to a conjecture of D. F. Anderson (Pacific J. Math. 1978, V. 79, № 1, P. 5–17) concerning freeness of finitely generated projective modules over normal monoid algebras. In the special case of torsion divisor class groups, or equivalently, the case of an integral extension, this conjecture was proved in 1982 (see Gubeladze, Generalized Serre problem for affine rings generated by monomials, Izdat. Tbiliss. Gos. Univ., Tbilisi, 1982, and Chouinard // Mich. Math. J. 1982. V. 29, № 2, P. 143–148). Using that result, the author obtains a description of the maximal class of commutative monoids satisfying the cancellation condition for which all finitely generated projective modules over the corresponding semigroup algebra (with any principal ideal domain as coefficient ring) are free. Namely, this class turns out to be the so-called “seminormal” monoids. By the same token a complete answer is given to some questions posed by Chouinard in the paper cited above.
Bibliography: 15 titles.