Related papers: Implications of positive formulas in modules (RIMS…

In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…

We show that, for positive definite kernels, if specific forms of regularity (continuity, Sn-differentiability or holomorphy) hold locally on the diagonal, then they must hold globally on the whole domain of positive-definiteness. This…

We provide explicit descriptions for the rational powers and Rees valuations of several classes of ideals invariant under natural actions of tori and products of general linear groups, in terms of polyhedra and lattice points. This allows…

We survey variety theory for modules of finite dimensional Hopf algebras, recalling some definitions and basic properties of support and rank varieties where they are known. We focus specifically on properties known for classes of examples…

We develop the basic model theory of local positive logic, a new logic that mixes positive logic (where negation is not allowed) and local logic (where models omit types of infinite distant pairs). We study several basic model theoretic…

We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.

Let $R$ be a commutative unital ring, $a\in R$ and $t$ a positive integer. $a^{t}$-reduced $R$-modules and universally $a^{t}$-reduced $R$-modules are defined and their properties given. Known (resp. new) results about reduced $R$-modules…

We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powers, and symbolic powers of monomial ideals. This…

Modular categories are important algebraic structures in a variety of subjects in mathematics and physics. We provide an explicit, motivated and elementary definition of a modular category over a field of characteristic 0 as an equivalence…

In this paper, we consider a wider class of simulation functions and present some coincidence and common fixed point results in metric spaces. Results obtained in this paper extend, generalize and unify some well-known fixed and common…

We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$. The question of which words have only positive eigenvalues is addressed. This question was raised some…

This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…

The category of mobi algebras has been introduced as a model to the unit interval of real numbers. The notion of mobi space over a mobi algebra has been proposed as a model for spaces with geodesic paths. In this paper we analyse the…

Positivity in $\ast$-algebras can be defined either algebraically, by quadratic modules, or analytically, by $\ast$-representations. By the induction procedure for $\ast$-representations we can lift the analytical notion of positivity from…

Let $M$ be a finitely generated module over a ring $\Lambda$. With certain mild assumptions on $\Lambda$, it is proven that $M$ is a reflexive $\Lambda$-module, once $M \cong M^{**}$ as a $\Lambda$-module.

We discuss tableaux for the Implicational Propositional Calculus and show how they may be used to establish its completeness.

We argue for a foundational epistemic claim and a hypothesis about the production and uses of mathematical epidemiological models, exploring the consequences for our political and socio-economic lives. First, in order to make the best use…

In this work, we focus on the use of influence functions to identify relevant training examples that one might hope "explain" the predictions of a machine learning model. One shortcoming of influence functions is that the training examples…

In this article, we study the notion of a finite $\Sigma$-Rickart module, as a module theoretic analogue of a right semi-hereditary ring. A module $M$ is called \emph{finite $\Sigma$-Rickart} if every finite direct sum of copies of $M$ is a…

Based on implicative involutive BE algebras, we redefine the orthomodular lattices, by introducing the notion of implicative-orthomodular lattices, and we study their properties. We characterize these algebras, proving that the…