In this paper, we build a dimension theory related to Shelah's 2-rank, dp-rank, and o-minimal dimension. We call this dimension op-dimension. We exhibit the notion of the n-multiorder property, generalizing the order property, and use this to create op-rank, which generalizes 2-rank. From this we build opdimension. We show that op-dimension bounds dp-rank, that opdimension is sub-additive, and ...

For any field F , we give an example of a prime finitely generated F -algebra of GK dimension 2 for which GK dimension is not finitely partitive. For each m ∈ {0, 1, 2, 3, . . .}∪{∞}, we give an example of a prime finitely generated F -algebra having GK dimension 2 which has classical Krull dimension m; the algebra of GK dimension 2 which has infinite classical Krull dimension has the additiona...

An `2 metric is a metric ρ such that √ ρ can be embedded isometrically into R endowed with Euclidean norm, and the minimal possible d is the dimension associated with ρ. A dimension reduction of an `2 metric ρ is an embedding of ρ into another ` 2 2 metric μ so that distances in μ are similar to those in ρ and moreover, the dimension associated with μ is small. Much of the motivation in investi...

There are remarkable relations between the graded homological dimensions and the ordinary homological dimensions. In this paper, we study the injective dimension of a complex of graded modules and derive its some properties. In particular, we define the $^*$dualizing complex for a graded ring and investigate its consequences.

An `2 metric is a metric ρ such that √ ρ can be embedded isometrically into R endowed with Euclidean norm, and the minimal possible d is the dimension associated with ρ. A dimension reduction of an `2 metric ρ is an embedding of ρ into another `2 metric μ so that distances in μ are similar to those in ρ and moreover, the dimension associated with μ is small. Much of the motivation in investigat...

‎In this paper we give an upper bound for Noetherian dimension of all injective modules with Krull dimension on arbitrary rings‎. ‎In particular‎, ‎we also give an upper bound for Noetherian dimension of all Artinian modules on Noetherian duo rings.

the purpose of this research is to prioritize the indexes of discretion, heterogeny and autogeny factors in order to analyze and evaluate their readiness for ideal situation of central bank of the islamic republic of iran (cbi). this research is an exploratory kind and in terms of method is a survey kind. the data collection tool is questionnaire. after two delphi cycles, in final questionnaire...

0. Introduction 1 1. General properties of the cohomological dimension 2 2. Bockstein theory 6 3. Cohomological dimension of Cartesian product 10 4. Dimension type algebra 15 5. Realization theorem 19 6. Test spaces 24 7. Infinite-dimensional compacta of finite cohomological dimension 28 8. Resolution theorems 33 9. Resolutions preserving cohomological dimensions 41 10. Imbedding and approximat...