in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.

In this paper, a new  algorithm for computing secondary invariants of  invariant rings of monomial groups is presented. The main idea is to compute simultaneously a truncated SAGBI-G basis and the standard invariants of the ideal generated by the set of primary invariants.  The advantage of the presented algorithm lies in the fact that it is well-suited to complexity analysis and very easy to i...

(t1, . . . , tn) ∈ C S2n = C[x1, . . . , xn, y1, . . . , yn], { xi −→ xi yi −→ tixi + yi, The restriction of this action to a general linear subspace G ⊂ C is called an action of Nagata type. In [M], generalizing the result of Nagata [N1] (r = 3 and n = 16), we proved the infinite generation of the invariant ring S in the case where the inequality 1/2+1/(n− r)+1/r ≤ 1 holds, where r is the codi...

We give a presentation for the (integral) torus-equivariant Chow ring of the quot scheme, a smooth compactification of the space of rational curves of degree d in the Grassmannian. For this presentation, we refine Evain’s extension of the method of Goresky, Kottwitz, and MacPherson to express the torus-equivariant Chow ring in terms of the torus-fixed points and explicit relations coming from t...

We extend knot contact homology to a theory over the ring Z[λ±1, μ±1], with the invariant given topologically and combinatorially. The improved invariant, which is defined for framed knots in S and can be generalized to knots in arbitrary manifolds, distinguishes the unknot and can distinguish mutants. It contains the Alexander polynomial and naturally produces a two-variable polynomial knot in...

In this article we provide the uniform construction of fields with all known u-invariants. We also obtain the new values for the u-invariant: 2 r + 1, for r > 3. The main tools here are the new discrete invariant of quadrics (so-called, elementary discrete invariant), and the methods of [15] (which permit to reduce the questions of rationality of elements of the Chow ring over the base field to...

For every rational homology 3–sphere with H1(M, Z) = (Z/2Z) n we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten–Reshetikhin–Turaev invariant at this root and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invari...

There is a special local ring [Formula: see text] of order without identity for the multiplication, defined by We study algebraic structure linear codes over that non-commutative ring, in particular their residue and torsion codes. introduce notion quasi self-dual Type IV codes, whose all codewords have even Hamming weight. weight enumerators these means invariant theory, classify them short le...

Constructive invariant theory was a preoccupation of many nineteenth century mathematicians, but the topic fell out of fashion in the early twentieth century. In the latter twentieth century the topic enjoyed a resurgence, partly due to its connections with the construction of moduli spaces in algebraic geometry and partly due to the development of computational algorithms suitable for implemen...

Traditionally, non-singular curves of a fixed genus g are classified in two categories, those which are hyperelliptic and those which are not. The first ones are usually considered to be the simplest, since their geometry relies on their Weierstra points and is condensed on a line. Thus, the hyperelliptic locus Mg of the corresponding moduli space Mg is easily described and well understood. See...