Related papers: Localization of tight closure in two-dimensional r…
Motivated by the experimental evidence of the Nagaoka ferromagnetism in quantum dot systems by Dehollain et al [1], we search for possible confirmation of such kind of ferromagnetism by analyzing the spin-resolved transport properties of a…
Among reduced Noetherian prime characteristic commutative rings, we prove that a regular ring is precisely one where finite intersection of ideals commutes with taking bracket powers. However, reducedness is essential for this equivalence.…
In this note, we use the theory of test ideals and Cartier algebras to examine the interplay between the tight and integral closures in a local ring of positive characteristic. Using work of Schwede, we prove the abundance of strong test…
Let $R$ be an excellent regular ring of dimension $d$ containing a field $K$ of characteristic zero. Let $I$ be an ideal in $R$. We show that $Ass \ H^{d-1}_I(R)$ is a finite set. As an application we show that if $I$ is an ideal of height…
Most of the investigations to date on tight-binding, quantum percolation models focused on the quantum percolation threshold, i.e., the analogue to the Anderson transition. It appears to occur if roughly 30% of the hopping terms are…
We give two different, statistically consistent definitions of the length l of a prime knot tied into a polymer ring. In the good solvent regime the polymer is modelled by a self avoiding polygon of N steps on cubic lattice and l is the…
In this paper, we introduce a strong property $(A)$ and we study the transfer of property $(A)$ and strong property $(A)$ in trivial ring extensions and amalgamated duplication of a ring along an ideal. We also exhibit a class of rings…
Let $(A,\mathfrak{m})$ be a complete Cohen-Macaulay local ring. Assume $A$ is not Gorenstein. We say $A$ is a Teter ring if there exists a complete Gorenstein ring $(B,\mathfrak{n})$ with $\dim B = \dim A$ and a surjective map $B…
Relativistic thick ring models are constructed using previously found analytical Newtonian potential-density pairs for flat rings and toroidal structures obtained from Kuzmin-Toomre family of discs. In particular, we present systems with…
In this paper we consider birational properties of ramification in excellent local rings. We extend earlier results of the author with Olivier Piltant to show that strong local monomialization is true along a valuation dominating a…
We investigate how one can detect the dualizing property for a chain complex over a commutative local noetherian ring R. Our focus is on homological properties of contracting endomorphisms of R, e.g., the Frobenius endomorphism when R…
This is a two-part article. In the first part, we study an alternative notion to Nagata rings. A Nagata ring is a Noetherian ring $R$ such that every finite $R$-algebra that is an integral domain has finite normalization. We replace the…
Necessary and sufficient conditions are given for the completed group algebras of a compact p-adic analytic group with coefficient ring the p-adic integers or the field of p elements to be prime, semiprime and a domain. Necessary and…
In two recent papers, the author has developed a theory of graded annihilators of left modules over the Frobenius skew polynomial ring over a commutative Noetherian ring $R$ of prime characteristic $p$, and has shown that this theory is…
We define the notion of normal A-schemes, and approximable A-schemes. Approximable A-schemes inherit many good properties of ordinary schemes. As a consequence, we see that the Zariski-Riemann space can be regarded in two ways -- either as…
Internal preneighbourhood spaces inside any finitely complete category with finite coproducts and proper factorisation structure were first introduced in my earlier paper. This paper proposes a closure operation on internal preneighbourhood…
The commuting probability of a finite ring $R$, denoted by $\Pr(R)$, is the probability that any two randomly chosen elements of $R$ commute. In this paper, we obtain several bounds for $\Pr(R)$ through a generalization of $\Pr(R)$.…
A simple tight-binding model is used to illustrate how the time dependence of a state vector can be obtained from all the eigenvalues and eigenvectors of the Hamiltonian. The behavior of the eigenvalues and eigenvectors is studied for…
Motivated by a question of Tsai-Tsui-Wang, we consider the rigidity of map from manifolds with positive Ricci curvature to manifolds with positive sectional curvature. We show that if the Ricci curvature of the domain dominates that of the…
We count numbers of tame frieze patterns with entries in a finite commutative local ring. For the ring $\mathbb{Z}/p^r\mathbb{Z}$, $p$ a prime and $r\in\mathbb{N}$ we obtain closed formulae for all heights. These may be interpreted as…