In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new concept of involutive monomial division which is defined for a monomial set. Such a division provides for each monomial the self-consistent separation of the whole set of variables into two disjoint subsets. They are cal...

In this paper we consider a free associative algebra on three generators over an arbitrary field K. Given a term ordering on the commutative polynomial ring on three variables over K, we construct uncountably many liftings of this term ordering to a monomial ordering on the free associative algebra. These monomial orderings are total well orderings on the set of monomials, resulting in a set of...

Ezra Miller and Bernd Sturmfels Department of Mathemati s, University of California, Berkeley CA 94720, USA enmiller math.berkeley.edu, bernd math.berkeley.edu Abstra t. Gr obner basis theory redu es questions about systems of polynomial equations to the ombinatorial study of monomial ideals, or stair ases. This arti le gives an elementary introdu tion to urrent resear h in this area. After re...

The interpolation step of Guruswami and Sudan’s list decoding of Reed-Solomon codes poses the problem of finding the minimal polynomial of an ideal with respect to a certain monomial order. An efficient algorithm that solves the problem is presented based on the theory of Gröbner bases of modules. In a special case, this algorithm reduces to a simple Berlekamp-Massey-like decoding algorithm.

We consider the polynomial algebra H∗(CP∞ ×CP∞;Fp) as a module over the mod p Steenrod algebra, A(p), p being an odd prime. We give a minimal set of generators consisting of monomials and characterise all such ‘monomial bases’.

In this article we study bases for projective monomial curves and the relationship between the basis and the set of generators for the defining ideal of the curve. We understand this relationship best for curves in P and for curves defined by an arithmetic progression. We are able to prove that the latter are set theoretic complete intersections.

In this article, we study Hilbert Series of non-Cohen-Maculay tangent cones for some 4-generated pseudo symmetric monomial curves. We show that the Function is nondecreasing by explicitly computing it. also compute standard bases these toric ideals.

Abstract We relate quantum degree cones, parametrizing PBW degenerations of quantized enveloping algebras, to (negative tight monomial) cones introduced by Lusztig in the study monomials canonical bases, K -theoretic for quiver representations, and some maximal prime tropical flag varieties.