Abstract
For a commutative ring R, assume that c is a nonzero element of Z(R) with the property that cZ(R) = {0}. A local ring R is called c-local if Z(R)2 = {0, c}, Z(R)3 = {0}, and xZ(R) = {0} implies x ∈ {0, c}. For any finite c-local ring (R, 𝔪), it is proved that the ideal m has a minimal generating set which has a c-partition. The structure and classification up to isomorphism of all finite commutative c-local rings with order greater than 25 are determined.
ACKNOWLEDGMENTS
This research is supported by the National Natural Science Foundation of China (Grant No. 10671122). The second author is also partly supported by a grant of Science and Technology Commission of Shanghai Municipality (STCSM No. 09XD1402500).
Notes
Communicated by I. Swanson.