数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1086-1092.doi: 10.1016/S0252-9602(10)60105-1
卢丹诚1|武同锁2
LU Dan-Cheng1, WU Tong-Suo2
摘要:
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.
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