Chaoling HUANG

507374

Extensions and s-comparability of exchange rings

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.

Anahtar Kelimeler:

Exchange rings, excellent extensions, s-comparability

Extensions and s-comparability of exchange rings

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.

Keywords:

Exchange rings, excellent extensions, s-comparability,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

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Extensions and s-comparability of exchange rings

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