# Answer to Question #24417 in Algebra for Siavosh

Question #24417

Show that :

1- If a module is integrally closed , then so its isomorphic copy .

2- Let M be a divisible projective R-module.Then R is integrally closed.

1- If a module is integrally closed , then so its isomorphic copy .

2- Let M be a divisible projective R-module.Then R is integrally closed.

Expert's answer

First statement is obvioussince isomorphism preserves all algebraic properties.

Second statement means that for any r in R we have M=rM and then M -projective

means that it is direct summand and thus rM is direct summand of free module

R^n, thus by criteria of integral element we have that R have to be intagrally

closed.

Second statement means that for any r in R we have M=rM and then M -projective

means that it is direct summand and thus rM is direct summand of free module

R^n, thus by criteria of integral element we have that R have to be intagrally

closed.

## Comments

## Leave a comment