Closure operators in the categories of modules. Part I (Weakly hereditary and idempotent operators)

• Veröffentlicht in: Algebra and Discrete Mathematics
• Datum: 2013
• 1. Verfasser: Kashu, A.I.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2013
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/152290
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Closure operators in the categories of modules. Part I (Weakly hereditary and idempotent operators) / A.I. Kashu // Algebra and Discrete Mathematics. — 2013. — Vol. 15, № 2. — С. 213–228. — Бібліогр.: 10 назв. — англ.

In this work the closure operators of a category of modules R-Mod are studied. Every closure operator C of R-Mod defines two functions F₁с and F₂с, which in every module M distinguish the set of C-dense submodules F₁с(M) and the set of C-closed submodules F₂с(M). By means of these functions three ty...