Correspondences of Coclosed Submodules

We establish an order-preserving bijective correspondence between the sets of coclosed elements of some bounded lattices related by suitable Galois connections. As an application, we deduce that if M is a finitely generated quasi-projective left R-module with S = End _R (M) and N is an M-generated left R-module, then there exists an order-preserving bijective correspondence between the sets of coclosed left R-submodules of N and coclosed left S-submodules of Hom _R (M, N).     

A generalization of the Mitchell Lemma: The Ulmer Theorem and the Gabriel–Popescu Theorem revisited

We prove a generalization of the Mitchell Lemma, and we show that it is a key lemma that can be used in order to deduce in a unified easier way several important results. Thus, the Ulmer Theorem, the generalized Gabriel–Popescu Theorem and the generalized Takeuchi Lemma are all consequences of the generalized Mitchell Lemma.     

Transfer of splitness with respect to a fully invariant short exact sequence in abelian categories

Abstract

We study the transfer via functors between abelian categories of the (dual) relative splitness of objects with respect to a fully invariant short exact sequence. We mainly consider fully faithful functors and adjoint pairs of functors. We deduce applications to Grothendieck categories, (graded) module categories and comodule categories.     

Relatively Extending Modules

We investigate a generalization of extending modules relative to a class of modules and a proper class of short exact sequences of modules.     

Rickart and Dual Rickart Objects in Abelian Categories

We introduce and study relative Rickart objects and dual relative Rickart objects in abelian categories. We show how our theory may be employed in order to study relative regular objects and (dual) relative Baer objects in abelian categories. We also give applications to module and comodule categories.     

Strongly Rickart objects in abelian categories: Applications to strongly regular and strongly Baer objects

We show how the theory of (dual) strongly relative Rickart objects may be employed in order to study strongly relative regular objects and (dual) strongly relative Baer objects in abelian categories. For each of them, we prove general properties, we analyze the behavior with respect to (co)products, and we study the transfer via functors. We also give applications to Grothendieck categories, (graded) module categories and comodule categories.     

Gruson-Jensen Duality for Idempotent Rings

It is known that if R is a ring with identity, and S and A ^op are the functor rings associated to the categories Mod(R) and Mod(R ^op ), respectively, then there is a duality between the categories of finitely presented objects of Mod(S ^op ) and Mod(A). We prove here this result in a more general case, namely when R is an idempotent ring, not necessarily having an identity, and when the categories Mod(R) of torsionfree and unitary right R-modules and Mod(R ^op ) of torsionfree and unitary left R-modules are locally finitely presented.     

Strongly Rickart objects in abelian categories

We introduce and study (dual) strongly relative Rickart objects in abelian categories. We prove general properties, we analyze the behaviour with respect to (co)products, and we study the transfer via functors. We also give applications to Grothendieck categories, (graded) module categories and comodule categories. Our theory of (dual) strongly relative Rickart objects may be employed in order to study strongly relative regular objects and (dual) strongly relative Baer objects in abelian categories.     

Heat transfer and hydraulic performance models for a family of aluminum plate heat exchanger with transversal offset strip fins

This paper presents the experimental analysis of aluminum BPHX, with dimensions of 215 × 80 × 61 mm, having transversal offset strip fins with two pitches of 5 and 6.8 mm using liquid to liquid to measure the heat transfer and pressure drop performance in the Reynolds range of transitional to turbulent regime [10³, 10⁴]. Firstly, the heat exchangers were tested using water on both sides. A heat transfer and friction coefficients empirical correlations were determined, and the resulted functions were compared with two other models presented in the literature. Secondly, the heat exchangers were measured using water and engine oil as hot fluid.     

Uniqueness of uniform decompositions in exact categories

Two uniqueness theorems on uniform decompositions due to Krause, Diracca and Facchini are extended from abelian categories to weakly idempotent complete exact categories. We give applications to (quasi-)abelian categories, finitely accessible additive categories and exactly definable additive categories.