Related papers: On basic and Bass quaternion orders
A (generalized) topological space is called an iso-dense space if the set of all its isolated points is dense in the space. The main aim of the article is to show in $\mathbf{ZF}$ a new characterization of iso-dense spaces in terms of…
We prove an integral version of the classical Albert-Brauer-Hasse-Noether theorem regarding quaternion algebras over number fields. Let $\mathfrak A$ be a quaternion algebra over a number field $K$ and assume that $\mathfrak A$ satisfies…
We consider definably complete and Baire expansions of ordered fields: every definable subset of the domain of the structure has a supremum and the domain can not be written as the union of a definable increasing family of nowhere dense…
We suggest an analog of the Bass-Quillen conjecture for smooth affinoid algebras over a complete non-archimedean field. We prove this in the rank-1 case, i.e. for the Picard group. For complete discretely valued fields and regular affinoid…
A ring $R$ is an elementary divisor ring if every matrix over $R$ admits a diagonal reduction. We further explore various stable like conditions on a bezout duo-domain under which it is an elementary divisor domain. Many known results are…
We call a function "constructible" if it has a globally subanalytic domain and can be expressed as a sum of products of globally subanalytic functions and logarithms of positively-valued globally subanalytic functions. Our main theorem…
If X is a sequentially complete locally convex space, then a quotient bounded operator T is regular (in the sense of Waelbroeck) if and only if it is a bounded element (in the sense of Allan) of the algebra of quotient bounded operators on…
Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements.…
In Sternfeld's work on Kolmogorov's Superposition Theorem appeared the combinatorial-geometric notion of a basic set and a certain kind of arrays. A subset $X \subset \mathbb R^n$ is basic if any continuous function $X\to \mathbb R$ could…
Given a module M over a ring R which has a grading by a semigroup Q, we present a spectral sequence that computes the local cohomology of M at any Q-graded ideal I in terms of Ext modules. This method is used to obtain finiteness results…
In connection to two recent publications of ours in Arch. Math. Basel (2021) and Acta Math. Hung. (2022), respectively, and in regard to the results obtained in Arch. Math. Basel (2012), we have the motivation to study the near property of…
We provide an algorithm that, given any order $O$ in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right $O$-ideals, including the non-invertible ones. The theory is developed for a…
A well-ordering principle is a principle of the form: If $X$ is well-ordered then $F(X)$ is well-ordered, where $F$ is some natural operator transforming linear orders into linear orders. Many important subsystems of Second-order Arithmetic…
Quaternion analysis is considered in full details where a new analyticity condition in complete analogy to complex analysis is found. The extension to octonions is also worked out.
A subscheme $X\subset \Bbb P^{n+3}$ of codimension $3$ is {\em Pfaffian} if it is the degeneracy locus of a skew-symmetric map $f:\cal{E}\spcheck(-t) @>>> \cal{E}$ with $\cal{E}$ a locally free sheaf of odd rank on $\Bbb P^{n+3}$. It is…
We continue to study the local well-posedness for higher order Benjamin-Ono type equations, especially fourth order equations. The proof is based on the energy methods with correction terms. Although one of correction terms can eliminate…
Let $\RR_S$ denote the expansion of the real ordered field by a family of real-valued functions $S$, where each function in $S$ is defined on a compact box and is a member of some quasianalytic class which is closed under the operations of…
Let $R$ be a semilocal Dedekind domain with fraction field $F$. We show that two hereditary $R$-orders in central simple $F$-algebras which become isomorphic after tensoring with $F$ and with some faithfully flat \'etale $R$-algebra are…
We give details of a formerly known relation between ternary quadratic forms and quaternion orders through the even Clifford algebra. Based on this and classifications of ternary quadratic forms we give a completely explicit classification…
We show that a strong well-based cylindrical algebraic decomposition P of a bounded semi-algebraic set is a regular cell decomposition, in any dimension and independently of the method by which P is constructed. Being well-based is a global…