王明生
Abstract
In Ref. [1], Yao demonstrates that the projective dimension of a simple module over a commutative Noetherian ring equals its injective dimension and characterizes the commutative ring possessing an injective simple module. In this note, we consider a similar problem and generalize the main result of Ref. [1].
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In Ref. [1], Yao demonstrates that the projective dimension of a simple module over a commutative Noetherian ring equals its injective dimension and characterizes the commutative ring possessing an injective simple module. In this note, we consider a similar problem and generalize the main result of Ref. [1].
Key concepts: Mathematics, Injective module, Simple module, Projective module, Module, Injective function, Global dimension, Dimension (graph theory)