Definition 1.1. A curved L∞ algebra over A consists of a locally free finitely generated graded A]-module V, together with a cohomological degree 1 and square zero derivation d : Ŝym(V∨[−1])→ Ŝym(V∨[−1]) where V∨ is the A]-linear dual and the completed symmetric algebra is also over A]. There are two additional requirements on the derivation d: (1) The derivation d makes Ŝym(V∨[−1]) into a dga ...

It is well known that for the case of a countable partial order, the ideal completion and the chain completion coincide. We investigate the boundary at which the chain and ideal completion do not coincide. We show in particular that the ideal completion is not sequentially adequate; that is it is not possible in general to simply replace the ideal completion with a completion based on sequences...

A finite lattice is interval dismantlable if it can be partitioned into an ideal and a filter, each of which can be partitioned into an ideal and a filter, etc., until you reach 1-element lattices. In this note, we find a quasi-equational basis for the pseudoquasivariety of interval dismantlable lattices, and show that there are infinitely many minimal interval non-dismantlable lattices. Define...

The Briançon-Skoda theorem appears in many variations in recent literature. The common denominator is that the theorem gives a sufficient condition that implies a membership φ ∈ a, where a is an ideal of some ring R. In the analytic interpretation R is the local ring of an analytic space Z, and the condition is that |φ| ≤ C|a| holds on the space Z. The theorem thus relates the rate of vanishing...

An old question of T. Jech and K. Prikry asks if an existence of a precipitous ideal implies necessary existence of a normal precipitous ideal. The aim of the paper is to prove some results in the positive direction. Thus, it is shown that under some mild assumptions, an existence of a precipitous ideal over א1 implies an existence of a normal precipitous ideal over א1 once a Cohen subset is ad...

the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

Let Q be an affine semigroup generating Z, and fix a finitely generated Z -graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z-graded injective resolution of M up to any desired cohomological degree. As an application, we derive an algorithm computing the local cohomology modulesH I(M) supported on any monomial (that is, Z -graded) ideal...

We show that every quasi-ordinary Weierstrass polynomial P (Z) = Z + a1(X)Z d−1 + · · ·+ ad(X) ∈ K[[X]][Z], X = (X1, . . . , Xn), over an algebraically closed field of characterisic zero K, such that a1 = 0, is ν-quasi-ordinary. That means that if the discriminant ∆P ∈ K[[X]] is equal to a monomial times a unit then the ideal (a i (X))i=2,...,d is monomial and generated by one of a i (X). We us...