Abstract
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(1)
Let N be a submodule of a finitely presented module M. Then N is finitely generated ⇔M/N is finitely presented.
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(2)
A direct sum of two finitely presented modules is a finitely presented module.
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(3)
If N1 and N2 are finitely presented submodules of a module M such that N1 + N2 is a finitely presented module, then N1 ∩ N2 is a finitely generated module.
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© 1998 Springer Science+Business Media Dordrecht
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Tuganbaev, A.A. (1998). Semihereditary and invariant rings. In: Semidistributive Modules and Rings. Mathematics and Its Applications, vol 449. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5086-6_7
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DOI: https://doi.org/10.1007/978-94-011-5086-6_7
Publisher Name: Springer, Dordrecht
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