Remarks on Absolutely Flat Rings

Abstract

A가 absolutely flat이고 항등원을 가진 가환노이더환이면 A는유한개 체(field)들이 직적(direct product)과 동형이다. 좀 더 일반적으로 A가 absolutely flat이고 항등원을 가진 가환환이면 A는 체들의 직적의 부분환 subdirect product와 동정이다.

Let A be a commutative, Noetherian and absolutely flat ring with identity. Then A is isomorphic to a direct product of a family of finitely many fields. In general, a commutative and absolutely flat ring with identity is isomorphic to a subdirect product of fields.

Let A be a commutative, Noetherian and absolutely flat ring with identity. Then A is isomorphic to a direct product of a family of finitely many fields. In general, a commutative and absolutely flat ring with identity is isomorphic to a subdirect product of fields.