Relative natural classes and relative injectivity
نویسندگان
چکیده
منابع مشابه
Relative natural classes and relative injectivity
Let τ be a hereditary torsion theory on the category R-Mod of left R-modules over an associative unitary ring R. We introduce the notion of τ-natural class as a class of modules closed under τ-dense submodules, direct sums, and τ-injective hulls. We study connections between certain conditions involving τ-(quasi-)injectivity in the context of τnatural classes, generalizing results established b...
متن کاملRelative Injectivity and Cs - Modules
In this paper we show that a direct decomposition of modules M N, with N homologically independent to the inJective hull of H, is a CS-module if and only if N is injective relative to H and both of M and N are CS-modules. As an application, we prove that a direct sum of a non-singular semisimple module and a quasi-continuous module with zero socle is quasi-continuous. This result is known for q...
متن کاملRelative Injectivity and Cs - Modules Mahmoud
In this paper we show that a direct decomposition of modules M N, with N homologically independent to the inJective hull of H, is a CS-module if and only if N is injective relative to H and both of M and N are CS-modules. As an application, we prove that a direct sum of a non-singular semisimple module and a quasi-continuous module with zero socle is quasi-continuous. This result is known for q...
متن کاملRelative semicharacteristic classes
§0. Introduction In 1973 Ronnie Lee introduced the notion of semicharacteristic classes, which are invariants of the bordism group yi^(Bn) of closed manifolds equipped with a free action of a finite group n. In this paper we relativize his theory. Associated to a homomorphism G->n of finite groups, there is the relative bordism group yim(BG-> Bn), which is the bordism group of compact manifolds...
متن کاملRelative Injectivity as Cocompleteness for a Class of Distributors
Notions and techniques of enriched category theory can be used to study topological structures, like metric spaces, topological spaces and approach spaces, in the context of topological theories. Recently in [D. Hofmann, Injective spaces via adjunction, arXiv:math.CT/0804.0326] the construction of a Yoneda embedding allowed to identify injectivity of spaces as cocompleteness and to show monadic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2005
ISSN: 0161-1712,1687-0425
DOI: 10.1155/ijmms.2005.671