A Raman spectroscopic study of aqueous solutions of KH,P04 as a function of concentration and temperature has been made. Attention is focused on the analysis of the bands arising from the internal modes of the H,P04-anions. The band profile of these internal modes has been analysed by a Fourier transform self-deconvolution method which allowed quantitative information about phosphate dimerization to he obtained. The results seem to indicate the existence of two different configurations for the dimers. The association constant for each dimer and their thermodynamic parameters were obtained from the spectroscopic data.
We report the complete genome sequences of four neurovirulent isolates of porcine rubulavirus (PorPV) from 2015 and one historical PorPV isolate from 1984 obtained by next-generation sequencing. A phylogenetic tree constructed using the individual sequences of the complete HN genes of the 2015 isolates and other historical sequences deposited in the GenBank database revealed that several recent neurovirulent isolates of PorPV (2008-2015) cluster together in a separate clade. Phylogenetic analysis of the complete genome sequences revealed that the neurovirulent strains of PorPV that circulated in Mexico during 2015 are genetically different from the PorPV strains that circulated during the 1980s.
Given a full subcategory [Fscr ] of a category [Ascr ], the existence of left [Fscr ]-approximations (or [Fscr ]-preenvelopes) completing diagrams in a unique way is equivalent to the fact that [Fscr ] is reflective in [Ascr ], in the classical terminology of category theory.In the first part of the paper we establish, for a rather general [Ascr ], the relationship between reflectivity and covariant finiteness of [Fscr ] in [Ascr ], and generalize Freyd's adjoint functor theorem (for inclusion functors) to not necessarily complete categories. Also, we study the good behaviour of reflections with respect to direct limits. Most results in this part are dualizable, thus providing corresponding versions for coreflective subcategories.In the second half of the paper we give several examples of reflective subcategories of abelian and module categories, mainly of subcategories of the form Copres (M) and Add (M). The second case covers the study of all covariantly finite, generalized Krull-Schmidt subcategories of {\rm Mod}_{R}, and has some connections with the “pure-semisimple conjecture”.1991 Mathematics Subject Classification 18A40, 16D90, 16E70.
The f o r m u l a dim(A+B)=dim(A)+dim(B)-dim(AnB) works when 'dim' s t a n d s f o r t h e dimension of subspaces A,B of a n y v e c t o r space. I n general, however, i t does n o longer hold if 'dim' m e a n s t h e uniform ( o r Goldie) dimension of submodules A,B of a module M over a ring R, and in f a c t t h e l e f t hand s i d e m a y b e i n f i n i t e while t h e r i g h t hand side i s f i n i t e . I n t h i s paper we s h a l l give a c h a r a c t e r i z a t i o n of t h o s e modules M i n which t h e f o r m u l a holds f o r a n y t w o submodules A$, a s well a s s o m e c o n d i t i o n s in t h e ring R which g u a r a n t e e t h a t dim(A+B) i s f i n i t e whenever A and B a r e f i n i t e dimensional R-modules. C u r r e n t a d d r e s s of t h e a u t h o r : Aiberto del Valle Departamento d e M a t e m a t i c a s Universidad d e Murcia 30.001 Murcia
Abstract. The category of left modules over right coherent rings of finite weak global dimension has several nice features. For example, every left module over such a ring has a flat cover (Belshoff, Enochs, Xu) and, if the weak global dimension is at most two, every left module has a flat envelope (Asensio, Martínez). We will exploit these features of this category to study its objects.In particular, we will consider orthogonal complements (relative to the extension functor) of several classes of modules in this category. In the case of a commutative ring we describe an idempotent radical on its category of modules which, when the weak global dimension does not exceed 2, can be used to analyze the structure of the flat envelopes and of the ring itself.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.