In this article, we study the k-Lefschetz properties for non-Artinian algebras, proving that several known results in Artinian case can be generalized setting. Moreover, describe how to characterize graded algebras having using sectional matrices. We then apply obtained of Jacobian algebra hyperplane arrangements, with particular attention class free arrangements.

Copyright q 2012 Derya Keskin T ¨ utüncü et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. It is proved that if L is a complete modular lattice which is compactly generated, then RadL/0 is Artinian if, and only if for every s...

Let $R$ be a commutative Noetherian ring and let $fa$, $fb$ be two ideals of $R$ such that $R/({fa+fb})$ is Artinian. Let $M$, $N$ be two finitely generated $R$-modules. We prove that $H_{fb}^j(H_{fa}^t(M,N))$ is Artinian for $j=0,1$, where $t=inf{iin{mathbb{N}_0}: H_{fa}^i(M,N)$ is not finitelygenerated $}$. Also, we prove that if $DimSupp(H_{fa}^i(M,N))leq 2$, then $H_{fb}^1(H_{fa}^i(M,N))$ i...

We reformulate the integrality property of the Poincaré inner product in the middle dimension, for an arbitrary Poincaré Q-algebra, in classical terms (discriminant and local invariants). When the algebra is 1-connected, we show that this property is the only obstruction to realizing it by a closed manifold, up to dimension 11. We reinterpret a result of Eisenbud and Levine on finite map germs,...

Let A be a standard graded Artinian K-algebra, with char K = 0. We prove the following. 1. A has the Weak Lefschetz Property (resp. Strong Lefschetz Property) if and only if Gr(z)(A) has the Weak Lefschetz Property (resp. Strong Lefschetz Property) for some linear form z of A. 2. If A is Gorenstein, then A has the Strong Lefschetz Property if and only if there exists a linear form z of A such t...

*Correspondence: [email protected] 2Otto-von-Guericke Universität, Magdeburg, Germany Full list of author information is available at the end of the article Abstract We describe an algorithm which finds binomials in a given ideal I ⊂ Q[x1, . . . , xn] and in particular decides whether binomials exist in I at all. Binomials in polynomial ideals can be well hidden. For example, the lowest degr...