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.
Keywords
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Details
| Primary Language | English |
|---|---|
| Subjects | Algebra and Number Theory |
| Journal Section | Research Article |
| Authors | |
| Submission Date | July 7, 2025 |
| Acceptance Date | September 5, 2025 |
| Publication Date | December 31, 2025 |
| Published in Issue | Year 2025 Volume: 6 Issue: 2 |
Cite
EBSCO | DOAJ |
Scilit | SOBIAD |