Jacobson's Lemma via Gr(o)bner-Shirshov Bases

• 来源期刊: 代数集刊（英文版）
• 关键词: inverse Gr(o)bner-Shirshov basis Jacobson's lemma
• 年，卷（期）: 2017,（2）
• 页码范围: 309-314
• 页数: 6页
• 语种: 英文
• DOI: 10.1142/S1005386717000189

摘要

Let R be a ring with identity 1.Jacobson's lemma states that for any a,b ∈ R,if 1-ab is invertible then so is 1-ba.Jacobson's lemma has suitable analogues for several types of generalized inverses,e.g.,Drazin inverse,generalized Drazin inverse,and inner inverse.In this note we give a constructive way via Gr(o)bner-Shirshov basis theory to obtain the inverse of 1-ab in terms of (1-ba)-1,assuming the latter exists.