相关论文: On the structure of quaternion rings over $\mathbb…

We consider the four structures $(\mathbb{Z}; \mathrm{Sqf}^\mathbb{Z})$, $(\mathbb{Z}; <, \mathrm{Sqf}^\mathbb{Z})$, $(\mathbb{Q}; \mathrm{Sqf}^\mathbb{Q})$, and $(\mathbb{Q}; <, \mathrm{Sqf}^\mathbb{Q})$ where $\mathbb{Z}$ is the additive…

We determine the quantum variance of a sequence of families of automorphic forms on a compact quotient arising from a non-split quaternion algebra. Our results compare to those obtained by Luo--Sarnak, Zhao, and Sarnak--Zhao on the modular…

We prove a higher dimensional generalization of Gross and Zagier's theorem on the factorization of differences of singular moduli. Their result is proved by giving a counting formula for the number of isomorphisms between elliptic curves…

We prove the main result that a groupoid of order n is an idempotent k-translatable quasigroup if and only if its multiplication is given by x.y = (ax+by)(mod n), where a+b = 1(mod n), a+bk = 0(mod n) and (k,n)= 1. We describe the structure…

We study the spectral geometry of the conformal Jacobi operator on a 4-dimensional Riemannian manifold (M,g). We show that (M,g) is conformally Osserman if and only if (M,g) is self-dual or anti self-dual. Equivalently, this means that the…

We construct Abelian model structures on the category of chain complexes over a ring $R$, from the notion homological dimensions of modules. Given an integer $n > 0$, we prove that the left modules over a ringoid $\mathfrak{R}$ with…

We extend the differential form representation of N = (n,n) supersymmetric quantum mechanics to the superconformal case. We identify the superalgebras occurring for n = 1,2,4, give necessary and sufficient conditions for their existence,…

In this paper some results on the Lie structure of prime superalgebras are discussed. We prove that, with the exception of some special cases, for a prime superalgebra, $A$, over a ring of scalars $\Phi$ with $1/2\in \Phi$, if $L$ is a Lie…

In this paper, we take the classic dihedral and quaternion groups and explore questions like "what if we replace $i=e^{2\pi i/4}$ in $Q_8$ with a larger root of unity?" and "what if we add a reflection to $Q_8$?" The delightful answers…

Motivated by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered $\lambda$-ring structures over a filtered ring from a purely algebraic point of view. From a global perspective, we first…

Inspired by the recent work by Nadji, Ahmia and Ram\'irez, we examined the arithmetic properties of $\bar{B}_{l_1,l_2} (n)$, the number of overpartitions of n whose parts are neither divisible by $l_1$ nor divisible by $l_2$. In particular,…

We construct a family of semiprimitive and non von Neumann regular rings satisfying that any right or left module is isomorphic to a quotient of its flat cover (in the sense of Enochs) by a small submodule. This answers in the negative a…

A conjecture of Coleman implies that only finitely many quaternion algebras over the rational numbers can be the endomorphism $\mathbf{Q}$-algebras of abelian surfaces over the complex numbers which can be defined over $\mathbf{Q}$. One may…

A Type IV-II Z4-code is a self-dual code over Z4 with the property that all Euclidean weights are divisible by eight and all codewords have even Hamming weight. In this paper we use generalized bent functions for a construction of…

A $1-$factorization of a complete graph on $2n$ vertices is said to be $G-$regular if it posseses an automorphism group $G$ acting sharply transitively on the vertex-set. The problem of determining which groups can realize such a situation…

Some comments are made on the matrices which serve as the basis of a quaternionic algebra. We show that these matrices are related with the quaternionic action of the imaginary units from the left and from the right.

We prove that every isometry of between (not-necessarily orthogonal) summands of a unimodular quadratic space over a semiperfect ring can be extended an isometry of the whole quadratic space. The same result was proved by Reiter for the…

The structures of cyclic DNA codes of odd length over the finite rings R=Z_{4}+wZ_{4}, w^{2}=2 and S=Z_{4}+wZ_{4}+vZ_{4}+wvZ_{4},w^{2}=2,v^{2}=v,wv=vw are studied. The links between the elements of the rings R, S and 16 and 256 codons are…

Let $(M, q)$ be a quadratic projective module of an odd rank over an commutative ring, where the form $q$ is semiregular, with global Witt index of at least $2$, and with $\mathrm{rk}(M) \ge 7$. We prove standard commutator formulae and…

We find a necessary condition for the existence of an action of a Lie group $G$ by quaternionic automorphisms on an integrable quaternionic manifold in terms of representations of $\mathfrak{g}$. We check this condition and prove that a…