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http://hdl.handle.net/10662/12251
Títulos: | A remark on prime ideals |
Autores/as: | Lee, S.C. Varmazyar, R. |
Palabras clave: | Prime ideal;Generalized prime submodule;Semiprime submodule;Weakly semiprime submodule;Ideal primordial;Submódulo principal generalizado;Submódulo Semiprime;Submódulo débilmente semiprime |
Fecha de publicación: | 2020 |
Editor/a: | Universidad de Extremadura |
Resumen: | If M is a torsion-free module over an integral domain, then we show that for each submodule N of M the envelope Eм(N) of N in M is an essential extension of N. In particular, if N is divisible then Eм(N) = N. The last condition says that N is a semiprime submodule of M if N is proper. Let M be a module over a ring R such that for any ideals a, b of R, (a ∩ b) M = aM ∩ bM. If N is an irreducible and weakly semiprime submodule o f M, then we prove that (N :ʀ M) is a prime ideal of R. As a result, we obtain that if p is an irreducible ideal of a ring R such that a² ⊆ p (a is an ideal of R) ⇒ a ⊆ p, then p is a prime ideal. |
URI: | http://hdl.handle.net/10662/12251 |
DOI: | 10.17398/2605-5686.35.1.43 |
Colección: | Extracta Mathematicae Vol. 35, nº 1 (2020) |
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