A Decomposition Theorem for Utumi and Dual-Utumi Modules
Bull. Korean Math. Soc. Published online August 26, 2021
Yasser Ibrahim and Mohamed F. Yousif
Cairo University, Egypt and Tiabah University, Saudi Arabia; Ohio State University
Abstract : We show that if M is a Utumi module, in particular if M is quasi-continuous, then M = Q⊕K, where Q is quasi-injective that is both a square-full as well as a dual-square-full module, K is a square-free module, and Q & K are orthogonal. Dually, we also show that if M is a Dual-Utumi module whose local summands are summands, in particular if M is quasi-discrete, then M = P⊕K where P is quasi-projective that is both a square-full as well as a dual-square-full module, K is a dual-square-free module, and P & K are factor-orthogonal.
Keywords : Utumi and Dual Utumi Modules, Quasi-injective and Quasi-Projective Modules, Square-Free and Dual-Square-Free Modules; Discrete and Quasi-Discrete modules; D3-modules and D4-modules