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.