Related papers: {\Gamma}-Abel-Grassmann's groupoids characterized …

A groupoid correspondence on an etale, locally compact groupoid induces a C*-correspondence on its groupoid C*-algebra. We show that the Cuntz-Pimsner algebra for this C*-correspondence relative to an ideal associated to an open invariant…

We determine the structure of completely inverse AG**-groupoids modulo semilattices of abelian groups and their involutive, idempotent-fixed automorphisms.

We consider the class $\mathcal{A}_0$ of Abelian block-rigid $CRQ$-groups of ring type. A subgroup $A$ of an Abelian group $G$ is called an \textsf{absolute ideal} of the group $G$ if $A$ is an ideal in any ring on $G$. We describe…

In this article, we describe the lattice of ideals of some Green biset functors. We consider Green biset functors which satisfy that each evaluation is a finite dimensional split semisimple commutative algebra and use the idempotents in…

Let $\Gamma$ be a discrete group. To every ideal in $\ell^{\infty}(\G)$ we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general…

Let kG be the completed group algebra of a uniform pro-p group G with coefficients in a field k of characteristic p. We study right ideals I in kG that are invariant under the action of another uniform pro-p group Gamma. We prove that if I…

In this paper, we introduce two new approximation properties for \'etale groupoids, almost elementariness and (ubiquitous) fiberwise amenability, inspired by Matui's and Kerr's notions of almost finiteness. In fact, we show that, in their…

Bergman has given the following abstract characterisation of the inner automorphisms of a group $G$: they are exactly those automorphisms of $G$ which can be extended functorially along any homomorphism $G \rightarrow H$ to an automorphism…

Every two-sided ideal $\mathfrak a$ in the integral group ring $\mathbb Z[G] $ of a group $G$ determines a normal subgroup $G \cap (1 + \mathfrak a)$ of $G$. In this paper certain problems related to the identification of such subgroups,…

We generalise the notion of a separating intersection of links (SIL) to give necessary and sufficient criteria on the defining graph $\Gamma$ of a right-angled Coxeter group $W_\Gamma$ so that its outer automorphism group is large: that is,…

Let A be a C*-algebra and I a closed two-sided ideal of A. We use the Hilbert C*-modules picture of the Cuntz semigroup to investigate the relations between the Cuntz semigroups of I, A and A/I. We obtain a relation on two elements of the…

Let $\Gamma^{+}$ be the positive cone in a totally ordered abelian group $\Gamma$, and $\alpha$ an action of $\Gamma^{+}$ by extendible endomorphisms of a $C^{\ast}$-algebra $A$. Suppose $I$ is an extendible $\alpha$-invariant ideal of $A$.…

We investigate modular embeddings for semi-arithmetic Fuchsian groups. First we prove some purely algebro-geometric or even topological criteria for a regular map from a smooth complex curve to a quaternionic Shimura variety to be covered…

In the first section of this paper, we introduce the notions of fractional and invertible ideals of semirings and characterize invertible ideals of a semidomain. In section two, we define Pr\"{u}fer semirings and characterize them in terms…

We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group $A(\Gamma)$ fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups $\text{Mod}(S)$. In…

Let $B \subseteq A$ be an inclusion of C$^*$-algebras. We study the relationship between the regular ideals of $B$ and regular ideals of $A$. We show that if $B \subseteq A$ is a regular C$^*$-inclusion and there is a faithful invariant…

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, we consider the intuitionistic fuzzification of the concept of sub-hyperquasigroups in a hyperquasigroup and…

We prove a sandwiching lemma for inner-exact locally compact Hausdorff \'etale groupoids. Our lemma says that every ideal of the reduced $C^*$-algebra of such a groupoid is sandwiched between the ideals associated to two uniquely defined…

The trace set of a Fuchsian group $\Gamma$ ist the set of length of closed geodesics in the surface $\Gamma \backslash \mathbb{H}$. Luo and Sarnak showed that the trace set of a cofinite arithmetic Fuchsian group satisfies the bounded…

Let $G$ be a non-compact semisimple Lie group with finite centre and finitely many components. We show that any finitely generated group $\Gamma$ which is quasi-isometric to an irreducible lattice in $G$ has the $R_\infty$-property, namely,…