Skip to main content
MathOverflow

Return to Question

added 11 characters in body
Source Link
My. A
My. A
  • 29
  • 2

We know that if $R $ is a domain then any localization of $R $ at any multiplicative subset of $R $ is indecomposable, that is, has nonno non trivial idempotents. Now let $R $ hasbe a commutative ring with 1 that has no non trivial idempotents commutative tING wit 1. I am looking for an additional condition on $R $ under which any localization $R_r $ to be indecomposable for each non nilpotent element $r\in R $.

Thanks for any help.

We know that if $R $ is a domain then any localization of $R $ at any multiplicative subset of $R $ is indecomposable, that is, has non non trivial idempotents. Now let $R $ has no non trivial idempotents commutative tING wit 1. I am looking for an additional condition on $R $ under which any localization $R_r $ to be indecomposable for each non nilpotent element $r\in R $.

Thanks for any help.

We know that if $R $ is a domain then any localization of $R $ at any multiplicative subset of $R $ is indecomposable, that is, has no non trivial idempotents. Now let $R $ be a commutative ring with 1 that has no non trivial idempotents. I am looking for an additional condition on $R $ under which any localization $R_r $ to be indecomposable for each non nilpotent element $r\in R $.

Thanks for any help.

Source Link
My. A
My. A
  • 29
  • 2

When localization is indecomposable

We know that if $R $ is a domain then any localization of $R $ at any multiplicative subset of $R $ is indecomposable, that is, has non non trivial idempotents. Now let $R $ has no non trivial idempotents commutative tING wit 1. I am looking for an additional condition on $R $ under which any localization $R_r $ to be indecomposable for each non nilpotent element $r\in R $.

Thanks for any help.