论文标题
在单位规范环中的广义佛兰德定理
The Generalized Flanders' Theorem in Unit-regular Rings
论文作者
论文摘要
令r为单位规范环，让a，b，c In R满足ABA = ACA。如果AC和BA是可逆的，我们证明AC与BA相似。此外，如果AC和BA是可逆的Drazin，那么它们的Drazin倒置是相似的。对于任何n \ times n复合物矩阵A，B，c带ABA = ACA，我们证明AC和BA在且仅当其K-Powers具有相同等级时相似。这些概括了Hartwig证明的已知佛兰德定理。
Let R be a unit-regular ring, and let a,b,c in R satisfy aba=aca. If ac and ba are group invertible, we prove that ac is similar to ba. Furthermore, if ac and ba are Drazin invertible, then their Drazin inverses are similar. For any n\times n complex matrices A,B,C with ABA = ACA ,we prove that AC and BA are similar if and only if their k-powers have the same rank. These generalize the known Flanders' theorem proved by Hartwig.
