相关论文: In praise of order units

Let $R$ be an associative ring with identity and let $N$ be a nil ideal of $R$. It is shown that units of $R/N$ can be lifted to units in $R$. Under some mild conditions on the ring, a procedure is given to determine those lifted units in a…

We introduce a notion of natural orderings of elements of finite connected quandles of order $n$. When the elements of such a quandle $Q$ are already ordered naturally, any automophism on $Q$ is a natural ordering. Although there are many…

In this study, it is proven that the universal equivalence of general linear groups (admitting the inverse-transpose automorphism) of orders greater than $2$, over local, not necessarily commutative rings with $1/2$, is equivalent to the…

We exhibit a functor from the category OUS of order unit spaces and positive, unit-preserving mappings into the category $\Prob$ of probabilistic models (test spaces with designated state spaces) and morphisms thereof. Restricted to any…

We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover…

The main result of this paper is that all antichains are finite in the poset of monomial ideals in a polynomial ring, ordered by inclusion. We present several corollaries of this result, both simpler proofs of results already in the…

We give an order-theoretic characterization of the JB-algebras among the complete order unit spaces in terms of the existence of an order-anti-automorphism of the interior of the cone that is homogeneous of degree -1. More geometrically, we…

This paper concerns the characterisation of second order marginals for random sets in a discrete setting. Under the instance of unit covariances, this problem possesses a combinatorial symmetry, exploited jointly in the companion paper to…

Let $I$ be an ideal of height $d$ in a regular local ring $(R,m,k=R/m)$ of dimension $n$ and let $\Omega$ denote the canonical module of $R/I$. In this paper we first prove the equivalence of the following: the non-vanishing of the edge…

We formulate a positivity conjecture relating the Verlinde ring associated with an untwisted affine Lie algebra at a positive integer level and a subcategory of finite-dimensional representations over the corresponding quantum affine…

In this paper we prove that every automorphism of the semigroup of invertible matrices with nonnegative elements over a linearly oredered associative ring on some specially defined subgroup concides with the composition of an inner…

We prove that $\Theta$-positive representations of fundamental groups of surfaces (possibly cusped or of infinite type) satisfy a collar lemma, and their associated cross-ratios are positive. As a consequence we deduce that…

A self-affine tiling of a compact set G of positive Lebesgue measure is its partition to parallel shifts of a compact set which is affinely similar to G. We find all polyhedral sets (unions of finitely many convex polyhedra) that admit…

We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal…

We show that the category of corings over a fixed base ring with local units is equivalent to the category of comonads in (right) unital modules whose underlying functors preserve inductive limits. Changing base rings, we prove a…

We study copositive matrices which admit a decomposition into a sum of a positive semidefinite matrix and a matrix with nonnegative entries. Our main result shows that if the off-diagonal entries of a copositive matrix are nondecreasing in…

We show that the orbit closure of a directing module is regular in codimension one. In particular, this result gives information about a distinguished irreducible component of a module variety.

We prove the following result. Let k be an infinite perfect field of positive characteristic and assume that strong resolution of singularities holds over k. Let R be a localization of a commutative d-dimensional k-algebra of finite type…

Let $KG$ be the group ring of a group $G$ over a commutative ring $K$ with unity. The rings $KG$ are described for which $xx^\sigma=x^\sigma x$ for all $x=\sum_{g\in G}\alpha_gg\in KG$, where \quad $x\mapsto x^\sigma=~\sum_{g\in…

The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring $\mathcal{R}$ with a unit…