Covering classes and 1-tilting cotorsion pairs over commutative rings

We are interested in characterising the commutative rings for which a 1-tilting cotorsion pair ( 𝒜 , 𝒯 ) {(\mathcal{A},\mathcal{T})} provides for covers, that is when the class 𝒜 {\mathcal{A}} is a covering class. We use Hrbek’s bijective correspondence between the 1-tilting cotorsion pairs over a commutative ring R and the faithful finitely generated Gabriel topologies on R. Moreover, we use results of Bazzoni–Positselski, in particular a generalisation of Matlis equivalence and their characterisation of covering classes for 1-tilting cotorsion pairs arising from flat injective ring epimorphisms. Explicitly, if 𝒢 {\mathcal{G}} is the Gabriel topology associated to the 1-tilting cotorsion pair ( 𝒜 , 𝒯 ) {(\mathcal{A},\mathcal{T})} , and R 𝒢 {R_{\mathcal{G}}} is the ring of quotients with respect to 𝒢 {\mathcal{G}} , we show that if 𝒜 {\mathcal{A}} is covering, then 𝒢 {\mathcal{G}} is a perfect localisation (in Stenström’s sense [B. Stenström, Rings of Quotients, Springer, New York, 1975]) and the localisation R 𝒢 {R_{\mathcal{G}}} has projective dimension at most one as an R-module. Moreover, we show that 𝒜 {\mathcal{A}} is covering if and only if both the localisation R 𝒢 {R_{\mathcal{G}}} and the quotient rings R / J {R/J} are perfect rings for every J ∈ 𝒢 {J\in\mathcal{G}} . Rings satisfying the latter two conditions are called 𝒢 {\mathcal{G}} -almost perfect.

Hubungan Antara Kelekatan Orang Tua Dengan Kedisiplinan Siswa Di Mts Nurul Huda Sedati

This research is a correlational quantitative method that is motivated by phenomena that seek to undiscipline in school environment. This study aims to determine whether there is a relationship between parents with discipline students in MTs Nurul Huda Sedati. Variables in this research is Parent attachment as independent variable (X) and Discipline as independent variable (Y). This research was conducted in MTs Nurul Huda Sedati covering class VII-IX with total sample of 221 students, taken using proporsionate stratified random sampling technique. Data collection in this research using psychological model that is Likert, that is IPPA scale (parent attachment) and disciplinary scale. Hypothesis in this research is there is positive relation between parent attachment with student discipline. Data analysis was done by statistical technique from Product Moment from Pearson using SPSS 18.0 for windows. The result of data analysis show open coefficient (rxy) = 0,285 with significance level 0.000 (less than 0,01) accepted hypothesis. The results showed there was a positive relationship between parents with discipline students in MTs Nurul Huda Sedati.

Quasi-cotilting modules and torsion-free classes

We prove that all quasi-cotilting modules are pure-injective and cofinendo. It follows that the class [Formula: see text] is always a covering class whenever [Formula: see text] is a quasi-cotilting module. Some characterizations of quasi-cotilting modules are given. As a main result, we prove that there is a bijective correspondence between the equivalent classes of quasi-cotilting modules and torsion-free covering classes.

Strict Mittag–Leffler modules over Gorenstein injective modules

In this paper, we study the conditions under which a module is a strict Mittag–Leffler module over the class [Formula: see text] of Gorenstein injective modules. To this aim, we introduce the notion of [Formula: see text]-projective modules and prove that over noetherian rings, if a module can be expressed as the direct limit of finitely presented [Formula: see text]-projective modules, then it is a strict Mittag–Leffler module over [Formula: see text]. As applications, we prove that if [Formula: see text] is a two-sided noetherian ring, then [Formula: see text] is a covering class closed under pure submodules if and only if every injective module is strict Mittag–Leffler over [Formula: see text].

Absolute purity in the category of quasi coherent sheaves

In this paper we consider the class of absolutely pure and Fp-injective quasi-coherent sheaves. We show that these two classes of quasi-coherent sheaves over a locally coherent scheme are equivalent. As a corollary we will show that the class of absolutely pure quasi-coherent sheaves over such a scheme is an enveloping and a covering class. It is proved that over a locally coherent scheme, the pair (?(Abs(X),Abs(X)) is a cotorsion theory. The existence of a duality between absolutely pure envelopes and flat covers is proved as expected.

On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity

Given a nonempty abstract set , and a covering class , and a finite, finitely subadditive outer measure , we construct an outer measure and investigate conditions for to be submodular. We then consider several other set functions associated with and obtain conditions for equality of these functions on the lattice generated by . Lastly, we describe a construction of a finite, finitely subadditive outer measure given an arbitrary family of subsets, , of and a nonnegative, finite set function defined on .

AVALIAÇÃO DO USO DA TERRA EM MICROBACIA UTILIZANDO UMA MATRIZ DE PARTIÇÃO FUZZY

AVALIAÇÃO DO USO DA TERRAEM MICROBACIA UTILIZANDO UMAMATRIZ DE PARTIÇÃO FUZZY Sérgio Campos1; Edson Luís Piroli2; Célia Regina Lopes Zimback3; João Batista Tolentino Rodrigues31Departamento de Engenharia Rural, Faculdade de Ciências Agronômicas, Universidade Estadual Paulista, Botucatu, SP, [email protected] Experimental de Rosana, Universidade Estadual Paulista, Rosana, SP3Departamento de Ciências do Solo, Faculdade de Ciências Agronômicas, Universidade Estadual Paulista, Botucatu, SP 1 RESUMO A evolução da informática oferece, hoje, a possibilidade de desenvolvimento de novas técnicas e metodologias para elaboração de trabalhos em todas as áreas do conhecimento humano. Aliado a isto, a capacidade de manuseio de grande volume de dados dos computadores pessoais atuais, facilita a criação e aplicação de novas ferramentas para análise de informações. Neste trabalho objetivou-se a aplicação de uma matriz de partição fuzzy para análise os dados obtidos pelo sensor TM do satélite Landsat 5, visando elaborar a classificação supervisionada do uso da terra na microbacia hidrográfica do Arroio das Pombas, no Município de Botucatu, SP. A atribuição de pesos no momento da criação das assinaturas, possibilitou que uma simples área de treinamento oferecesse entrada em mais de uma classe de cobertura. Constatou-se, também, uma modificação no resultado da classificação quando comparada com a classificação por máxima verossimilhança, principalmente com relação à maior homogeneidade e melhor definição das bordas das classes. UNITERMOS: matrix de partição fuzzy, classificação supervisionada, imagem de satélite. CAMPOS, S., PIROLI, E.L., ZIMBACK, C.R.L., RODRIGUES, J.B.T.ANALYSIS OF SOIL USE IN A MICROBASIN USING A FUZZY PARTITION MATRIX 2 ABSTRACT Informatics evolution presently offers the possibility of new technique and methodology development for studies in all human knowledge areas. In addition, the present personal computer capacity of handling a large volume of data makes the creation and application of new analysis tools easy. This paper aimed the application of a fuzzy partition matrix to analyze data obtained from the Landsat 5 TMN sensor, in order to elaborate the supervised classification of land use in Arroio das Pombas microbasin, in Botucatu,SP,Brazil. It was possible that one single training area present input in more than one covering class due to weight attribution at the signature creation moment. A change in the classification result was also observed when compared to maximum likelihood classification, mainly when related to bigger uniformity and better class edges classification.KEYWORDS: fuzzy partition matrix, supervised classification, satellite image.

Conormal morphisms

This article represents another step in our programme of obtaining a Galois theory and a coGalois theory when we have a category C and a given enveloping (for Galois) or covering (for coGalois) class. More precisely, in this paper, we study what should be understood by a conormal morphism between two objects of a given category and we characterize conormal morphisms between finite abelian groups when the covering class under consideration is that of torsion-free abelian groups.

On the Complete Regularity of Some Category Spaces

A category space is a measure space which is also a topological space, the measure and the topology being related by ‘a set is measurable iff it has the Baire property’ and ‘a set is null iff it is nowhere dense’ [4]. We considered some category spaces in [3]; now we show that if a null set is deleted from the space, then the topology can be taken to be completely regular. The essential part of the construction consists of obtaining a suitable refinement of the original sequential covering class and using the consequent strong upper density function to define the required topology. Then the complete regularity follows much as in [1].

On Strong Upper Densities

Let ψ be the outer measure generated by a gauge g and a sequential covering class C of closed sets of a metric space X, and let D be the resulting strong upper density function. That is, for each A ⊆ X and each x ∈ X:the infimum being taken over all countable subcollections {Iα} of C such that and, for all Iα in the subcollection, d(Iα) < ε where d(Iα) is the diameter of d(Iα).