### A remark on the Hilbert series of tranversal polymatroids.

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An algorithm is described which computes generators of the kernel of derivations on k[X₁,...,Xₙ] up to a previously given bound. For w-homogeneous derivations it is shown that if the algorithm computes a generating set for the kernel then this set is minimal.

We study when the modifications of the Cohen-Macaulay vertex cover ideal of a graph are Cohen-Macaulay.

Let $G$ be a group with identity $e$ and let $R$ be a $G$-graded ring. In this paper, we introduce and study the concept of graded $(2,n)$-ideals of $R$. A proper graded ideal $I$ of $R$ is called a graded $(2,n)$-ideal of $R$ if whenever $rst\in I$ where $r,s,t\in h\left(R\right)$, then either $rt\in I$ or $rs\in Gr\left(0\right)$ or $st\in Gr\left(0\right)$. We introduce several results concerning $gr$-$(2,n)$-ideals. For example, we give a characterization of graded $(2,n)$-ideals and their homogeneous components. Also, the relations between graded $(2,n)$-ideals and others that already exist, namely, the graded prime ideals,...

We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra 𝔤𝔩(1|2).

Let k be a field, let $$G$$ be a finite group. We describe linear $$G$$ -gradings of the polynomial algebra k[x 1, ..., x m] such that the unit component is a polynomial k-algebra.

We present an example which confirms the assertion of the title.

The class of loop spaces of which the mod $p$ cohomology is Noetherian is much larger than the class of $p$-compact groups (for which the mod $p$ cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as $\u2102{P}^{\infty}$ and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space $BX$ of such an object and prove it is as small as expected, that is, comparable to that of $B\u2102{P}^{\infty}$. We also show that $B$X differs basically from the classifying space of a $p$-compact group...

Known results on the generalized Davenport constant relating zero-sum sequences over a finite abelian group are extended for the generalized Noether number relating rings of polynomial invariants of an arbitrary finite group. An improved general upper degree bound for polynomial invariants of a non-cyclic finite group that cut out the zero vector is given.