Year: 2025
Type: article
Abstract: In this paper, we study the behavior of modules possessing the Summand Sum Essential Property (SSEP) in the context of trivial extensions of rings. We provide a detailed examination of how the SSEP and the classical Summand Sum Property (SSP) are preserved or characterized when extending a ring by an (R, R)-bimodule. Necessary and sufficient conditions are established under which the trivial extension inherits these properties from the base ring. Our results generalize existing findings on summand properties and contribute to a deeper understanding of module decompositions and essentiality in extended algebraic structures. Several illustrative examples are provided to demonstrate the applicability of the theoretical developments.
Authors: Eren Doğan, Mustafa Alkan
Institutions: Hakkari University, Akdeniz University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7118323355