On Gröbner Bases in Monoid and Group Rings
ثبت نشده
چکیده
منابع مشابه
Finite Gröbner Bases in Infinite Dimensional Polynomial Rings and Applications
We introduce the theory of monoidal Gröbner bases, a concept which generalizes the familiar notion in a polynomial ring and allows for a description of Gröbner bases of ideals that are stable under the action of a monoid. The main motivation for developing this theory is to prove finiteness results in commutative algebra and applications. A basic theorem of this type is that ideals in infinitel...
متن کاملOn quasi-Armendariz skew monoid rings
Let $R$ be a unitary ring with an endomorphism $σ$ and $F∪{0}$ be the free monoid generated by $U={u_1,…,u_t}$ with $0$ added, and $M$ be a factor of $F$ setting certain monomial in $U$ to $0$, enough so that, for some natural number $n$, $M^n=0$. In this paper, we give a sufficient condition for a ring $R$ such that the skew monoid ring $R*M$ is quasi-Armendariz (By Hirano a ring $R$ is called...
متن کاملComputing the Additive Structure of Indecomposable Modules over Dedekind-like Rings Using Gröbner Bases
We introduce a general constructive method to find a p-basis (and the Ulm invariants) of a finite Abelian p-group M . This algorithm is based on Gröbner bases theory. We apply this method to determine the additive structure of indecomposable modules over the following Dedeking-like rings: ZCp, where Cp is the cyclic group of order a prime p, and the p−pullback {Z→ Zp ← Z} of Z⊕ Z.
متن کاملGröbner Bases and Betti Numbers of Monoidal Complexes
Combinatorial commutative algebra is a branch of combinatorics, discrete geometry, and commutative algebra. On the one hand, problems from combinatorics or discrete geometry are studied using techniques from commutative algebra; on the other hand, questions in combinatorics motivated various results in commutative algebra. Since the fundamental papers of Stanley (see [13] for the results) and H...
متن کاملGröbner Bases over Finitely Generated Affine Monoids and Applications. The Direct Sum Case
For multidimensional linear systems with constant coefficients, Gröbner bases are the universal tool to solve algorithmically a multitude of problems which arise in control theory. Gröbner bases are defined over the polynomial ring which means that the domain of definition of discrete systems is the positive orthant. However, often the individual variables are interpreted diversely, e.g., some ...
متن کامل