Related papers: A short note on containment of cores
We study the ring extensions R \subseteq T having the same set of prime ideals provided Nil(R) is a divided prime ideal. Some conditions are given under which no such T exist properly containing R. Using idealization theory, the examples…
This paper is wrong and is therefore withdrawn.
In this paper we prove that small cancellation rings under some natural restrictions are non-amenable and contain non-commutative free associative algebra.
We study zero divisors and minimal prime ideals in semirings of characteristic one. Thereafter we find a counterexample to the most obvious version of primary decomposition, but are able to establish a weaker version. Lastly, we study…
IMPORTANT NOTE: This paper is much rougher than I'd usually submit, and not entirely complete, though the main theorems and proofs should not be hard to follow. Given the ongoing strike at UK Universities it may be some time before I get to…
Given a radical ideal $I$ in a regular ring $R$, the Containment Problem of symbolic and ordinary powers of $I$ consists of determining when the containment $I^{(a)} \subseteq I^b$ holds. By work of Ein-Lazersfeld-Smith, Hochster-Huneke and…
Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics. Structural completeness and decidability of…
The main point of Clarke and Strong's comment, namely that our results concerning the effect of integrability on the hopping of electrons between chains are probably not related to the notion of coherence proposed in \cite{clarke}, is…
We establish a criterion for the (failure of) the containment $I^{(m)}\subset I^r$ for 3-generated ideals $I$ defining reduced sets of points in $\mathbb{P}^2$. Our criterion arises from studying the minimal free resolutions of the powers…
We prove that Global Choice is not conservative over ZC and that ZF $-$ Union does not prove existence of $x \cup y$ for all $x$ and $y$. Each proof is by constructing a pathological model inside a symmetric extension of $L.$
Observations of pre-/proto-stellar cores in young star-forming regions show them to be mass segregated, i.e. the most massive cores are centrally concentrated, whereas pre-main sequence stars in the same star-forming regions (and older…
An argument is given which exhibits color confinement in nonabelian gauge theory.
We establish new classes of Ratliff-Rush closed ideals and some pathological behavior of the Ratliff-Rush closure. In particular, Ratliff-Rush closure does not behave well under passage modulo superficial elements, taking powers of ideals,…
We prove that there exists a 1-convex surface whose universal covering does not satisfy the discrete disk property.
We point out that in processes involving the parton content of the photon the usual effective photon approximation should be modified. The reason is that the parton content of virtual photons is logarithmically suppressed compared to real…
This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).
We describe a perfect group whose localization is not perfect.
If s and t are relatively prime positive integers we show that the s-core of a t-core partition is again a t-core partition
This note looks at two mistakes in the paper "Some characterizations of the ideals Ea which are discrete" by Khabaoui et al., published in "Rend. Circ. Mat. Palermo, II. Ser 72, 1325-1336 (2023)".
Let n be finite >2. We show that any class between S\Nr_n\CA_{n+3} and RCA_n is not atom canonical, and any class containing the class of completely representable algebras and contained in S_c\Nr_n\CA_{n+3} is not elementary. We show that…