Related papers: On the methods to construct UFD counterexamples to…

In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding…

Let A be a ring of dimension d and let P be a projective A-module of rank d. We prove that if for every finite extension R of A, R^d is cancellative, then P is cancellative. This gives an alternate proof of Bhatwadekar's result: every…

We construct rings of typed ordered fuzzy numbers whose component functions are of a common form. As this ring also contains improper fuzzy numbers (OFNs whose membership "functions" are actually just relations), we develop a set of…

We construct minimal $m$-dimensional immersions in $\R^{m+1}$, equipped with a $C^{1, \alpha}$ metric, $\alpha\in [0,1)$, with a sequence of \emph{catenoidal necks} or \emph{floating disks} converging to an isolated, multiplicity $2$,…

We propose a method to construct a variety of partition identities at once. The main application is an all-moduli generalization of some of Andrews' results in [5]. The novelty is that the method constructs solutions to functional equations…

Let $(Q, \mathfrak{n})$ be a regular local ring and let $f_1, \ldots, f_c \in \mathfrak{n}^2$ be a $Q$-regular sequence. Set $(A, \mathfrak{m}) = (Q/(\mathbf{f}), \mathfrak{n}/(\mathbf{f}))$. Further assume that the initial forms $f_1^*,…

In this paper we consider tiling $\{p, q \}$ of the Euclidean space and of the hyperbolic space, and its dual graph $\Gamma_{q, p}$ from a combinatorial point of view. A substitution $\sigma_{q, p}$ on an appropriate finite alphabet is…

Topological field theories and holomorphic field theories naturally appear in both mathematics and physics. However, there exist intriguing hybrid theories that are topological in some directions and holomorphic in others, such as twists of…

Let $k$ be a field, $m$ a positive integer, $\mathbb{V}$ an affine subvariety of $\mathbb{A}^{m+3}$ defined by a linear relation of the form $x_{1}^{r_{1}}\cdots x_{m}^{r_{m}}y=F(x_{1}, \ldots , x_{m},z,t)$, $A$ the coordinate ring of…

We obtain a partial classification of the finite groups $G$ for which the integral group ring $\mathbb{Z} G$ has projective cancellation, i.e. for which $P \oplus \mathbb{Z} G \cong Q \oplus \mathbb{Z} G$ implies $P \cong Q$ for projective…

Let $\mathbb{F}_q[T]$ be the polynomial ring over a finite field $\mathbb{F}_q$. We study the endomorphism rings of Drinfeld $\mathbb{F}_q[T]$-modules of arbitrary rank over finite fields. We compare the endomorphism rings to their subrings…

If $f$ is an idempotent in a ring $\Lambda$, then we find sufficient \linebreak conditions which imply that the cohomology rings $\oplus_{n\ge 0}Ext^n_{\Lambda}(\Lambda/{\br},\Lambda/{\br})$ and \linebreak $\oplus_{n\ge 0}Ext^n_{f\Lambda…

We revisit the possibility of constructing non-invertible topological defects for the axial symmetry of massless QED, despite its ABJ anomaly. Dressing the defects with a topological quantum field theory with mixed $U(1)$ and…

Motivated by the idea of using simple macroscopic examples to illustrate the physics of complex systems, we modify a historic experimental setup in which interacting floating magnets spontaneously self-assemble into ordered clusters. By…

We show the existence of new stable ring-like localized scalar field configurations whose stability is due to a combination of topological and nontopological charges. In that sense these defects may be called semitopological. These rings…

We present several new examples of reflection principles which apply to both class groups of number fields and picard groups of of curves over $\mathbb{P}^{1}/\mathbb{F}_{p}$. This proves a conjecture of Lemmermeyer about equality of 2-rank…

In this article we establish equivariant isomorphisms of Ext and Tor modules over different relative complete intersections. More precisely, for a commutative ring $Q$, this paper investigates how $Ext_{Q/(\boldsymbol{f})}^*(M,N)$ and…

$U(N)^{\otimes r} \otimes O(N)^{\otimes q}$ invariants are constructed by contractions of complex tensors of order $r+q$, also denoted $(r,q)$. These tensors transform under $r$ fundamental representations of the unitary group $U(N)$ and…

Let $f$ be a homeomorphism of the closed annulus $A$ isotopic to the identity, and let $X\subset {\rm Int}A$ be an $f$-invariant continuum which separates $A$ into two domains, the upper domain $U_+$ and the lower domain $U_-$. Fixing a…

Let R be a regular ring essentially of finite type over a perfect field k. An R-module M is called a unit R[F]-module if it comes equipped with an isomorphism F*M-->M where F denotes the Frobenius map on Spec R, and F* is the associated…