Simple-separable modules
Copyright policy )Simple-separable modules
A module $M$ over a ring is called simple-separable if every simple submodule of $M$ is contained in a finitely generated direct summand of $M$. While a direct sum of any family of simple-separable modules is shown to be always simple-separable, we prove that a direct summand of a simple-separable module does not inherit the property, in general. It is also shown that an injective module $M$ over a right noetherian ring is simple-separable if and only if $M=M_1 \oplus M_2$ such that $M_1$ is separable and $M_2$ has zero socle. The structure of simple-separable abelian groups is completely described.
- Abdelmalek Essaâdi University Morocco
Study of properties and structures of commutative rings, Deformations and Structures of Hom-Lie Algebras, Free, projective, and flat modules and ideals in associative algebras, separable module, Separable space, Epistemology, Separable module;simple-separable module;V-ring;$\pi$-V-ring, Mathematical analysis, Cebir ve Sayı Teorisi, Fuzzy Logic and Residuated Lattices, V-ring, FOS: Mathematics, General module theory in associative algebras, Algebra and Number Theory, FOS: Clinical medicine, Other classes of modules and ideals in associative algebras, Computer science, FOS: Philosophy, ethics and religion, Philosophy, \(\pi\)-V-ring, Computational Theory and Mathematics, Dentistry, Physical Sciences, Computer Science, Simple (philosophy), Medicine, simple-separable module, Calculus (dental), Modal Logics, Mathematics
Study of properties and structures of commutative rings, Deformations and Structures of Hom-Lie Algebras, Free, projective, and flat modules and ideals in associative algebras, separable module, Separable space, Epistemology, Separable module;simple-separable module;V-ring;$\pi$-V-ring, Mathematical analysis, Cebir ve Sayı Teorisi, Fuzzy Logic and Residuated Lattices, V-ring, FOS: Mathematics, General module theory in associative algebras, Algebra and Number Theory, FOS: Clinical medicine, Other classes of modules and ideals in associative algebras, Computer science, FOS: Philosophy, ethics and religion, Philosophy, \(\pi\)-V-ring, Computational Theory and Mathematics, Dentistry, Physical Sciences, Computer Science, Simple (philosophy), Medicine, simple-separable module, Calculus (dental), Modal Logics, Mathematics
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