 # ag.algebraic geometry – Infinite uniform dimension \$Rightarrow\$ infinitely many idempotents in a localization of a quotient Answer

Hello expensive customer to our community We will proffer you an answer to this query ag.algebraic geometry – Infinite uniform dimension \$Rightarrow\$ infinitely many idempotents in a localization of a quotient ,and the respond will breathe typical via documented info sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning in regards to the respond to this query.

ag.algebraic geometry – Infinite uniform dimension \$Rightarrow\$ infinitely many idempotents in a localization of a quotient

In common, it isn’t workable to bear such an model $$I$$ and component $$r in R setminus I$$ out of your assumption.

An clear obstruction is the category of rings of innumerable uniform dimension having precisely one prime model. If a hoop $$R$$ has a exclusive prime model, then the identical is undoubted of each nonzero quotient and localization. In specific, $$R$$ does not have any idempotents, nor does any ring ensuing from $$R$$ by quotients and localizations.

On the opposite hand, it is simple to bear rings with a exclusive prime model which too have innumerable uniform dimension. You can simply adjoin an innumerable variety of mutually orthogonal nilpotents to a bailiwick, e.g. $$R = okay[x_1, x_2, ldots]/ (x_{i}x_j)_{0 leq i leq j}$$ accommodates $$bigoplus_i x_iR$$.

we’ll proffer you the answer to ag.algebraic geometry – Infinite uniform dimension \$Rightarrow\$ infinitely many idempotents in a localization of a quotient query by way of our community which brings all of the solutions from a number of dependable sources.