# A clarification about the meaning of “Let $\mathbb{Z}$ be *the* trivial $G$-module”.

I have a question regarding a definition/lemma in the book from Charles A. Weibel, "An introduction to Homological Algebra". At page 161, there is a claim starting as follows:

Let $A$ be any $G$-module, and let $\mathbb{Z}$ the trivial $G$-module...

Question: how does exactly mean "let $\mathbb{Z}$ the trivial $G$-module"? Have I to read it as "...and let's consider the ordinary ring $\mathbb{Z}$ as a $G$-module with the trivial action", or as something else that I am missing?

Thanks for the useful clarification.

• It means $\mathbb{Z}$ the abelian group (not ring) with the trivial $G$-action. – Qiaochu Yuan Jun 7 '15 at 19:05
• "The trivial module $\mathbb{Z}$" means "the module $\mathbb{Z}$, with trivial action. So the article "the" refers to the module - the module. The is only one $\mathbb{Z}$. – Dietrich Burde Jun 7 '15 at 19:05