Semihereditary and invariant rings
Let N be a submodule of a finitely presented module M. Then N is finitely generated ⇔M/N is finitely presented.
A direct sum of two finitely presented modules is a finitely presented module.
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.
KeywordsPrime Ideal Division Ring Regular Element Nilpotent Element Minimal Prime Ideal
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