F-supplemented modules

• Published in: Algebra and Discrete Mathematics
• Date: 2020
• Main Author: Özdemir, S.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188555
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: F-supplemented modules / S. Özdemir // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 83–96. — Бібліогр.: 6 назв. — англ.

Let R be a ring, let M be a left R-module, and let U, V, F be submodules of M with F proper. We call V an F-supplement of U in M if V is minimal in the set F ⊆ X ⊆ M such that U+X = M, or equivalently, F ⊆ V , U+V = M and U∩V is F-small in V . If every submodule of M has an F-supplement, then we ca...