EXTENSION OF SQUARE STABLE EXCHANGE RINGS

作者：Abdolyousefi, Marjan Sheibani; Chen, Huanyin^*

来源：Mathematical Reports, 2017, 19(3): 281-291.

• square stable ideal
• exchange ideal
• regular ideal

An ideal I of a ring R is square stable if aR + bR = R with a is an element of I, b is an element of R implies that a(2) + by is an element of R is invertible for a y is an element of R. We prove that an exchange ideal I of a ring R is square stable if and only if for any a is an element of I, a(2) is an element of J(R) implies that a is an element of J(R) if and only if every regular element in I is strongly regular. This extends main characterization of exchange rings of square stable range one. Further, we prove that a regular ideal I of a ring R is square stable if and only if eRe is strongly regular for all idempotents e is an element of I if and only if aR + bR = R with a is an element of 1 + I, b is an element of R implies that a(2) + by is an element of U(R) for a y is an element of R. As a consequence, we prove that every square stable regular ideal is strongly separative.

• 出版日期2017
• 单位杭州师范大学; 中华女子学院