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Some properties of Z-small prime modules | ||
| Journal of University of Anbar for Pure Science | ||
| Volume 19, Issue 1 - Serial Number 19, May and June 2025, Pages 299-303 PDF (620.16 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.37652/juaps.2024.152157.1293 | ||
| Authors | ||
| Alaa Abbas Elewi* ; ِAya Salman | ||
| Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq; | ||
| Abstract | ||
| Let R be a commutative ring with identity, and H be a unital (left) E-module. In this paper, we give a new properties of Z-small modules. Where an E-module H is a Z-small prime module if and only if ann H = ann K, for every non-zero submodule K of H such that K ≪_Z H. Where a submodule K of an E-module H is called Z-small (briefly K ≪ _Z H) if K+B=H with B ⊇ Z_2 (E) and B is a submodule of H, then B =H. Among of these properties if H is finitely generated faithful multiplication E-module, then H is a small Z-small prime E-module if and only if E is a Z-small prime ring. Also, we prove that an E-module H is a Z-small prime if and only if E-module the E-module E / (ann H) is cogenerated by every non-trivial Z-small submodule of H. | ||
| Keywords | ||
| Small submodule; Z-Small submodule; prime modules | ||
| References | ||
|
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