Relative natural classes and relative injectivity | Zendy

Septimiu Crivei | Zendy

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Relative natural classes and relative injectivity

Author(s) -

Septimiu Crivei

Publication year - 2005

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/ijmms.2005.671

Subject(s) - mathematics , unitary state , associative property , natural number , injective function , class (philosophy) , pure mathematics , discrete mathematics , combinatorics , algebra over a field , arithmetic , computer science , artificial intelligence , political science , law

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 τ-natural classes, generalizing results established by S. S. Page and Y. Q. Zhou(1994) for natural classes

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