Mathematics – Rings and Algebras
Scientific paper
2006-01-23
J. Algebra 308 (2007), 44-62
Mathematics
Rings and Algebras
21 pages, 0 figures
Scientific paper
Let G be a finite group that acts on an abelian monoid A. If f: A -> G is a map so that f(a f(a)(b)) = f(a)f(b), for all a, b in A, then the submonoid S = {(a, f(a)) | a in A} of the associated semidirect product of A and G is said to be a monoid of IG-type. If A is a finitely generated free abelian monoid of rank n and G is a subgroup of the symmetric group Sym_n of degree n, then these monoids first appeared in the work of Gateva-Ivanova and Van den Bergh (they are called monoids of I-type) and later in the work of Jespers and Okninski. It turns out that their associated semigroup algebras share many properties with polynomial algebras in finitely many commuting variables. In this paper we first note that finitely generated monoids S of IG-type are epimorphic images of monoids of I-type and their algebras K[S] are Noetherian and satisfy a polynomial identity. In case the group of fractions of S also is torsion-free then it is characterized when K[S] is a maximal order. It turns out that they often are, and hence these algebras again share arithmetical properties with natural classes of commutative algebras. The characterization is in terms of prime ideals of S, in particular G-orbits of minimal prime ideals in A play a crucial role. Hence, we first describe the prime ideals of S. It also is described when the group of fractions is torsion-free.
Goffa Isabel
Jespers Eric
No associations
LandOfFree
Monoids of IG-type and Maximal Orders does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Monoids of IG-type and Maximal Orders, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Monoids of IG-type and Maximal Orders will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-601774