Related papers: On the Set of $t$-Linked Overrings of an integral …

For R a bounded triply connected domain with boundary consisting of disjoint Jordan loops there exists an operator T on a complex Hilbert space H so that the closure of R is a spectral set for T, but T does not dilate to a normal operator…

We study the conditions under which a TTF class in a module category over a ring is silting. Using the correspondence between idempotent ideals over a ring and TTF classes in the module category, we focus on finding the necessary and…

Let $R$ be a Mori domain with complete integral closure $\widehat R$, nonzero conductor $\mathfrak f = (R \ :\ \widehat R)$, and suppose that both $v$-class groups $\mathcal C_v (R)$ and $\mathcal C_v (\widehat R)$ are finite. If…

We prove an analogue of the Affine Horrocks' Theorem for local complete intersection ideals of height $n$ in $R[T]$, where $R$ is a regular domain of dimension $d$, which is essentially of finite type over an infinite perfect field of…

This paper seeks ring-theoretic conditions of an integral domain R that reflect in the Clifford property or Boolean property of its class semigroup S(R), that is, the semigroup of the isomorphy classes of the nonzero (integral) ideals of R…

The ultrapower $T^{\ast}$ of an arbitrary ordered set $T$ is introduced as an infinitesimal extension of $T$. It is obtained as the set of equivalence classes of the sequences in $T$, where the corresponding relation is generated by an…

We find necessary and sufficient conditions for a complete local ring containing the rationals to be the completion of a countable excellent local (Noetherian) domain. Furthermore, we find necessary and sufficient conditions for a complete…

An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…

The critical field behavior of a layered Ising superconductor with finite number of layers is studied. Under in-plane magnetic fields, the finite-momentum superconductivity dubbed as the orbital Fulde- Ferrell-Larkin-Ovchinnikov state is…

We characterize which complete local (Noetherian) rings T containing the rationals are the completion of a countable excellent local ring S. We also discuss the possibilities for the map from the minimal prime ideals of T to the minimal…

It is well-known that if R is a domain with finite character, each locally principal nonzero ideal of R is invertible. We address the problem of understanding when the converse is true and survey some recent results.

Let R be a differential domain finitely generated over a differential field, F, with field of constants, C, of characteristic 0. Let E be the quotient field of R. The paper investigates necessary and sufficient conditions on R's…

It is proved that if $D$ is a $UFD$ and $R$ is a $D$-algebra, such that $U(R)\cap D\neq U(D)$, then $R$ has a maximal subring. In particular, if $R$ is a ring which either contains a unit $x$ which is not algebraic over the prime subring of…

We let R be an o-minimal expansion of a field, V a convex subring, and $(R_0, V_{0})$ an elementary substructure of (R,V). We let L be the language consisting of a language for R, in which R has elimination of quantifiers, and a predicate…

We study the set of localizations of an integral domain from a topological point of view, showing that it is always a spectral space and characterizing when it is a proconstructible subspace of the space of all overrings. We then study the…

We prove that a local domain $R$, essentially of finite type over a field, is regular if and only if for every regular alteration $\pi : X \to Spec R$, we have that $R \pi_* \mathcal{O}_X$ has finite (equivalently zero in characteristic…

Let R be a commutative noetherian ring. Lindo and Pande have recently posed the question asking when every ideal of R is isomorphic to some trace ideal of R. This paper studies this question and gives several answers. In particular, a…

The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…

We study uO convergence on infinitely distributive lattices, extending key properties known from Riesz spaces. We show that order continuity of uO convergence characterizes infinite distributivity. We examine O-adherence and uO adherence of…

We study when $R \to S$ has the property that prime ideals of $R$ extend to prime ideals or the unit ideal of $S$, and the situation where this property continues to hold after adjoining the same indeterminates to both rings. We prove that…