The cyclic homology of an exact category was defined by R. McCarthy [17] using the methods of F. Waldhausen [26]. McCarthy’s theory enjoys a number of desirable properties, the most basic being the extension property, i.e. the fact that when applied to the category of finitely generated projective modules over an algebra it specializes to the cyclic homology of the algebra. However, we show tha...

Let k be an algebraically closed field, let R be an associative kalgebra, and let F = {Mα : α ∈ I} be a family of orthogonal points in Mod(R) such that EndR(Mα) ∼= k for all α ∈ I. Then Mod(F), the minimal full subcategory of Mod(R) which contains F and is closed under extensions, is a full exact Abelian sub-category of Mod(R) and a length category in the sense of Gabriel [8]. In this paper, we...

Economic reality is constituted by economic objects such as goods, commodities, money, value, price, and exchange which together give rise to the complex entity known as the market. Each of these categories is governed by exact laws that provide the conditions for settling objectively whether individuals’ views about an instance of any category indeed correspond to that category. This paper des...

Let f : G → A be a surjective homomorphism of transitive groupoid schemes and let L denote the kernel of f . The exact sequence of groupoid schemes 1 → L → G → A → 1 induces a sequence of functors between the categories of finite representations of these groupoid schemes Repf (A) → Repf (G) → Repf (L). We show that the category Repf (L) is a quotient category of Repf (G) by Repf (A) in an appro...

We consider a homology theory h : T → A on a triangulated category T with values in a graded abelian category A . If the functor h reflects isomorphisms, is full and is such that for any object x in A there is an object X in T with an isomorphism between h(X) and x, we prove that A is a hereditary abelian category, all idempotents in T split and the kernel of h is a square zero ideal which as a...

We consider a homology theory h : T ! A on a triangulated category T with values in a graded abelian category A . If the functor h re ects isomorphisms, is full and is such that for any object x in A there is an object X in T with an isomorphism between h(X) and x, we prove that A is a hereditary abelian category, all idempotents in T split and the kernel of h is a square zero ideal which as a ...

This paper presents a batch classifier that splits dataset into tree branches depending on the category type. It has been improved from earlier version and fixed mistake in paper. Two important changes have made. The first is to represent each with separate classifier. Each then classifies its own subset of data rows, using input values create centroid also itself. If contains more than one how...

abstract: aim and background: the exact review of the prevalence of internalized and externalized disorders in adolescence is essential to design and prepares appropriate remedial services that aimed at reducing the negative consequences and subsequent growth of mental disorders and improving adolescent functioning. the aim of this study is investigation of prevalence of internalized and extern...