Let S be a ring extension of R. In this note, for any positive integer s we study s-comparability related to ring extensions. We show that if S is an excellent extension of R, R and S are exchange rings, and R has the n-unperforation property. R satisfies s-comparability if and we only if so does S, and we prove that for a 2-sided ideal J of S, and an exchange subring R of the exchange ring S, which contains J as a direct summand, then R satisfies s-comparability if and only if so does R/J.
"Extensions and s-comparability of exchange rings,"
Turkish Journal of Mathematics: Vol. 36:
4, Article 5.
Available at: https://journals.tubitak.gov.tr/math/vol36/iss4/5