This paper can be seen as a continuation of the works contained in the recent preprints [Za], of the second author, and [Mi], of Juan Migliore. Our results are: 1). There exist codimension three artinian level algebras of type two which do not enjoy the Weak Lefschetz Property (WLP). In fact, for e ≫ 0, we will construct a codimension three, type two h-vector of socle degree e such that all the...

This paper can be seen as a continuation of the works contained in the recent preprints [Za], of the second author, and [Mi], of Juan Migliore. Our results are: 1). There exist codimension three artinian level algebras of type two which do not enjoy the Weak Lefschetz Property (WLP). In fact, for e ≫ 0, we will construct a codimension three, type two h-vector of socle degree e such that all the...

For an arbitrary left Artinian ring R, explicit descriptions are given of all the left denominator sets S of R and left localizations SR of R. It is proved that, up to R-isomorphism, there are only finitely many left localizations and each of them is an idempotent localization, i.e. SR ≃ S e R and ass(S) = ass(Se) where Se = {1, e} is a left denominator set of R and e is an idempotent. Moreover...

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...

The present work investigates the learnability of classes of substructures of some algebraic structure: submonoids and subgroups of some given group, ideals of some given commutative ring, subbelds of a vector space. The learner sees all positive data but no negative one and converges to a program enumerating or computing the set to be learned. Besides semantical (BC) and syntactical (Ex) conve...