Preradicals, closure operators in R-Mod and connection between them

• Published in: Algebra and Discrete Mathematics
• Date: 2014
• Main Author: Kashu, A.I.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2014
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/153348
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Preradicals, closure operators in R-Mod and connection between them / A.I. Kashu // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 86–96. — Бібліогр.: 6 назв. — англ.

For a module category R-Mod the class PR of preradicals and the class CO of closure operators are studied. The relations between these classes are realized by three mappings: Φ : CO → PR and Ψ₁, Ψ₂ : PR → CO. The impact of these mappings on the operations in PR and CO (meet, join, product, coproduct...