PURE-INJECTIVES RELATIVE TO A COTORSION PAIR: APPLICATIONS

AbstractFinitely accessible categories naturally arise in the context of the classical theory of purity. In this paper we generalise the notion of purity for a more general class and introduce techniques to study such classes in terms of indecomposable pure injectives related to a new notion of purity. We apply our results in the study of the class of flat quasi-coherent sheaves on an arbitrary scheme.

Download Full-text

A GENERALIZATION OF THE THEORY OF STANDARDLY STRATIFIED ALGEBRAS I: STANDARDLY STRATIFIED RINGOIDS

Glasgow Mathematical Journal ◽

10.1017/s0017089520000476 ◽

2020 ◽

pp. 1-36

Author(s):

O. MENDOZA ◽

M. ORTÍZ ◽

C. SÁENZ ◽

V. SANTIAGO

Keyword(s):

Classical Theory ◽

General Class ◽

General Setting ◽

Finite Dimensional ◽

Classical Notion ◽

Hereditary Algebras

Abstract We extend the classical notion of standardly stratified k-algebra (stated for finite dimensional k-algebras) to the more general class of rings, possibly without 1, with enough idempotents. We show that many of the fundamental results, which are known for classical standardly stratified algebras, can be generalized to this context. Furthermore, new classes of rings appear as: ideally standardly stratified and ideally quasi-hereditary. In the classical theory, it is known that quasi-hereditary and ideally quasi-hereditary algebras are equivalent notions, but in our general setting, this is no longer true. To develop the theory, we use the well-known connection between rings with enough idempotents and skeletally small categories (ringoids or rings with several objects).

Download Full-text

Let all social partners in the social support process count: New perspectives on classical theory

PsycEXTRA Dataset ◽

10.1037/e577572014-567 ◽

2013 ◽

Author(s):

Liu-Qin Yang ◽

Robert R. Wright ◽

Liu-Qin Yang ◽

Lisa M. Kath ◽

Michael T. Ford ◽

...

Keyword(s):

Social Support ◽

Classical Theory ◽

The Social ◽

Social Partners

Download Full-text

The Calder´on-Zygmund Theory I: Ellipticity

10.23943/princeton/9780691162515.003.0001 ◽

2017 ◽

Author(s):

Brian Street

Keyword(s):

Classical Theory ◽

Singular Integral ◽

Singular Integrals ◽

Differential Operators ◽

Integral Operators ◽

Singular Integral Operators ◽

Single Parameter ◽

Partial Differential ◽

Translation Invariant ◽

Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

Download Full-text