Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A class $\mathcal{C}$ of $R$-modules is called

-separative if $A \oplus A \simeq A \oplus B \simeq B \oplus B$ implies $A \simeq B$ for each $A,B \in \mathcal{C}$

-cancelative if $A \oplus C \simeq B \oplus C$ implies $A \simeq B$ for all $A,B,C \in \mathcal{C}$.

According to literature, if $R$ is commutative then the class of finitely generated projectives over $R$ is separative iff it is cancelative. Even though I keep finding it as 'easy to see' in literature I seem unable to prove separative => cancelative. I would be grateful for any hint.

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.