| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4664418 | Acta Mathematica Scientia | 2010 | 7 Pages |
Abstract
A commutative ring R is called extending if every ideal is essential in a direct summand of RR. The following results are proved: (1) C(X) is an extending ring if and only if X is extremely disconnected; (2) Spec(R) is extremely disconnected and R is semiprime if and only if R is a nonsingular extending ring; (3) Spec(R) is extremely disconnected if and only if R/N(R) is an extending ring, where N(R) consists of all nilpotent elements of R. As an application, it is also shown that any Gelfand nonsingular extending ring is clean.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
