Related papers: A short note on containment of cores
In this work we extend the concept of the Lipschitz saturation of an ideal defined in [5] to the context of modules in some different ways, and we prove they are generically equivalent.
We present preservation theorems for countable support iteration of nep forcing notions satisfying ``old reals are not Lebesgue null'' and ``old reals are not meager''. (Nep is a generalization of Suslin proper.) We also give some results…
We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.
The neural rings and ideals as an algebraic tool for analyzing the intrinsic structure of neural codes were introduced by C.~Curto et al. in 2013. Since then they were investigated in several papers, including the 2017 paper by…
An elementary embedding $j:M\rightarrow N$ between two inner models of ZFC is cardinal preserving if $M$ and $N$ correctly compute the class of cardinals. We look at the case $N=V$ and show that there is no nontrivial cardinal preserving…
We show that for ideals primary to a maximal ideal in a normal domain of finite type over the complex numbers, its tight closure is contained inside the continuous closure.
The containment problem for symbolic and ordinary powers of ideals asks for what values of $a$ and $b$ we have $I^{(a)} \subseteq I^b$. Over a regular ring, a result by Ein-Lazarsfeld-Smith, Hochster-Huneke, and Ma-Schwede partially answers…
For a number of starless cores, self-absorbed molecular line and column density observations have implied the presence of large-amplitude oscillations. We examine the consequences of these oscillations on the evolution of the cores and the…
We consider the polynomial ring in finitely many variables over an algebraically closed field of positive characteristic, and initiate the systematic study of ideals preserved by the action of the general linear group by changes of…
Let G be a group and H be a subgroup of G which is either finite or of finite index in G. In this note, we give some characterizations for normality of H in G. As a consequence we get a very short and elementary proof of the Main Theorem of…
Let R be an integral domain and I a nonzero ideal of R. A sub-ideal J of I is a t-reduction of I if (JI^{n})_{t}=(I^{n+1})_{t} for some positive integer n. An element x in R is t-integral over I if there is an equation x^{n} + a_{1}x^{n-1}…
It is proved that the ring $R$ with center $Z(R)$, such that the module $R_{Z(R)}$ is an essential extension of the module $Z(R)_{Z(R)}$, is not necessarily right quasi-invariant, i.e., maximal right ideals of the ring $R$ are not…
We introduce the idea of (s,t)-closure and delta-sets and show that (s,t)-closed beta-sets which are contained set-wise in (s,t)-closed delta-sets are also contained partition-wise. This implies the maximal (s,t)-core partition theorem of…
It is pointed out that current conservation alone does not suffice to prove Hara's theorem as it was claimed recently. By explicit calculation we show that the additional implicit assumption made in such "proofs" is that of a sufficiently…
The paper has been withdrawn by the author due to unhappy mistake in the initial scope of the work.
We give a detailed microscopic analysis of why holes are different from electrons in condensed matter. Starting from a single atom with zero, one and two electrons, we show that the spectral functions for electrons and for holes are…
Reduced ideals have been defined in the context of integer rings in quadratic number fields, and they are closely tied to the continued fraction algorithm. The notion of this type of ideal extends naturally to number fields of higher…
In this paper we examine the commutativity of ideal extensions. We introduce methods of constructing such extensions, in particular we construct a noncommutative ring T which contains a central and idempotent ideal I such that T/I is a…
We calculate the evolution of cloud cores embedded in different envelopes to investigate environmental effects on the mass accretion rate onto protostars. As the initial state, we neglect the magnetic field and cloud rotation, and adopt…
We discuss the lifetimes and evolution of dense cores formed as turbulent density fluctuations in magnetized, isothermal molecular clouds. We consider numerical simulations in which we measure the cores' magnetic criticality and Jeans…