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 $r$,...

We prove a theorem on the magnetic energy minimum in a system of perfect, or ideal, conductors. It is analogous to Thomson’s theorem on the equilibrium electric field and charge distribution in a system of conductors. We first prove Thomson’s theorem using a variational principle. Our new theorem is then derived by similar methods. We find that magnetic energy is minimized when the current dist...

In this paper we prove a strong Hahn-Banach theorem: separation of disjoint convex sets by linear forms is possible without any further conditions, if the target field R is replaced by a more general real closed extension field. From this we deduce a general Positivstellensatz for ∗-algebras, involving representations over real closed fields. We investigate the class of group algebras in more d...

Interior-point methods for nonlinear programming have been demonstrated to be quite efficient, especially for large scale problems, and, as such, they are ideal candidates for solving the nonlinear subproblems that arise in the solution of mixed-integer nonlinear programming problems via outer approximation. However, traditionally, infeasible primal-dual interior-point methods have had two main...

We show the existence of a unital subalgebra Pn of the symmetric group algebra linearly spanned by sums of permutations with a common peak set, which we call the peak algebra. We show that Pn is the image of the descent algebra of type B under the map to the descent algebra of type A which forgets the signs, and also the image of the descent algebra of type D. The algebra Pn contains a two-side...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ‎ring of continuous real-valued functions on $l$‎. ‎we show that the‎ ‎lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a‎ ‎normal coherent yosida frame‎, ‎which extends the corresponding $c(x)$‎ ‎result of mart'{i}nez and zenk‎. ‎this we do by exhibiting‎ ‎$zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$‎, ‎the‎ ‎...

This article investigates the codimension of commutator spaces [I, B(H)] of operator ideals on a separable Hilbert space, i.e., “How many traces can an ideal support?” We conjecture that the codimension can be only zero, one, or infinity. Using the arithmetic mean (am) operations on ideals introduced in [13] and the analogous arithmetic mean operations at infinity (am-∞) that we develop extensi...

Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.