Ideal-comparability over Regular Rings

We introduce the concept of ideal-comparability condition for regular rings. Let I be an ideal of a regular ring R. If R satisfies the I-comparability condition, then R is one-sided unit-regular if and only if so is R/I. Also, we show that a regular ring R satisfies the general comparability if and only if the following hold： （1） R/I satisfies the general comparability; （2） R satisfies the general I-comparability condition; （3） The natural map B（R） → B（R/I） is surjective.