We establish a general criterion for the finite presentability of subdirect products of groups and use this to characterize finitely presented residually free groups. We prove that, for all n ∈ N, a residually free group is of type FPn if and only if it is of type Fn. New families of subdirect products of free groups are constructed, including the first examples of finitely presented subgroups ...

A continuum means a compact connected metric space. For a positive integer n, a continuum X is said to be n-equivalent provided that X contains exactlyn topologically distinct subcontinua. A continuumX is said to be hereditarily n-equivalent provided that each nondegenerate subcontinuum of X is n-equivalent. If there exists a positive integer n such that X is n-equivalent, then X is said to be ...

The concept of finitely additive supermartingales, originally due to Bochner, is revived and developed. We exploit it to study measure decompositions over filtered probability spaces and the properties of the associated Doléans-Dade measure. We obtain versions of the Doob Meyer decomposition and, as an application, we establish a version of the Bichteler and Dellacherie theorem with no exogenou...

Fuzzy equality relations or indistinguishability operators generalize the concepts of crisp equality and equivalence relations in fuzzy systems where inaccuracy and uncertainty is dealt with. They generate fuzzy granularity and are an essential tool in Computing with Words (CWW). Traditionally, the degree of similarity between two objects is a number between 0 and 1, but in many occasions this ...

Every computable universal algebra has a finitely presented expansion, but there are examples of finitely generated, computably enumerable universal algebras with no finitely presented expansions. It is natural to ask whether such examples can be found in well-known classes of algebras such as groups and semigroups. In this paper, we build an example of a finitely generated, infinite, computabl...

In this paper we describe finitely generated groups H universally equivalent (with constants from G in the language) to a given torsion-free relatively hyperbolic group G with free abelian parabolics. It turns out that, as in the free group case, the group H embeds into the Lyndon’s completion G of the group G, or, equivalently, H embeds into a group obtained from G by finitely many extensions ...

Let $R$ be a commutative ring. In this paper we assert some properties of finitely generated comultiplication modules and Fitting ideals of them.