A note on lattices of idempotents in algebras
Journal
Publicationes Mathematicae-Debrecen
Journal Volume
86
Journal Issue
1��2��
Pages
183-186
Date Issued
2015
Author(s)
Abstract
Let R be a unital algebra over a field K.For idempotents e, f ? R, we define e ? f if and only if ef = e = f e.Let e ? f and e ? f denote the infimum and supremum of e and f , respectively, if they exist.Let e �� := 1 -e for an idempotent e ? R. We prove the following theorem: Let e, f ? R be nontrivial idempotents.Suppose that there exists p(�f) ? K [�f] with zero constant term such that p(ef ) = p(f e) and p(1) = 1.Then e ? f = p(ef ) and e ? f = 1 -p(e �� f �� ).
Type
journal article