【摘 要】
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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 fo
【机 构】
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Department of Mathematics, Huizhou University Huizhou, Guangdong 516007, China
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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.
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