Divisibility properties in semigroup rings.
نویسندگان
چکیده
منابع مشابه
Divisibility Properties of Group Rings over Torsion-free Abelian Groups
Let G be a torsion-free abelian group of type (0, 0, 0, . . . ) and R an integrally closed integral domain with quotient field K. We show that every divisorial ideal (respectively, t-ideal) J of the group ring R[X;G] is of the form J = hIR[X;G] for some h ∈ K[X;G] and a divisorial ideal (respectively, t-ideal) I of R. Consequently, there are natural monoid isomorphisms Cl(R) ∼= Cl(R[X;G]) and C...
متن کاملIdentities of Regular Semigroup Rings
The author proves that, if S is an FIC-semigroup or a completely regular semigroup, and if RS is a ring with identity, then R < E(S) > is a ring with identity. Throughout this paper, R denotes as a ring with identity. Let S be a semigroup, X ⊆ S . The following notations are used in the paper: < X > : the subsemigroup of S generated by X ; |X| : the cardinal number of X ; E(S): the set of idemp...
متن کاملDivisorial Linear Algebra of Normal Semigroup Rings
We investigate the minimal number of generators μ and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the semigroup. The main result is that for every bound C there exist, up to isomorphism, only finitely divisorial ideals I such that μ(I) ≤ C. It follows that there...
متن کاملDivisibility Properties by Multisection
The/?-adic order, vp(r), of r is the exponent of the highest power of a prime/? which divides r. We characterize the/?-adic order vp(Fn) of the F„ sequence using multisection identities. The method of multisection is a helpful tool in discovering and proving divisibility properties. Here it leads to invariants of the modulo p Fibonacci generating function for p ^ 5. The proof relies on some sim...
متن کاملA Regularity Criterion for Semigroup Rings
An analogue of the Kunz-Frobenius criterion for the regularity of a local ring in a positive characteristic is established for general commutative semigroup rings. Let S be a commutative semigroup (we always assume that S contains a neutral element), and K a field. For every m 6 Z+ the assignment x H-» x, x £ S, induces a K-endomorphism 7m of the semigroup ring R = K[S]. Therefore we can consid...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1974
ISSN: 0026-2285
DOI: 10.1307/mmj/1029001210