Left APP differential polynomial rings |
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Authors: | A. R. Nasr-Isfahani |
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Affiliation: | 1. Department of Mathematics, University of Isfahan, Isfahan, Iran;2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Irannasr_a@sci.ui.ac.ir nasr@ipm.ir |
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Abstract: | A ring R is called a left APP-ring if for each element a∈R, the left annihilator lR(Ra) is right s-unital as an ideal of R or equivalently R∕lR(Ra) is flat as a left R-module. In this paper, we show that for a ring R and derivation δ of R, R is left APP if and only if R is δ-weakly rigid and the differential polynomial ring R[x;δ] is left APP. As a consequence, we see that if R is a left APP-ring, then the nth Weyl algebra over R is left APP. Also we define δ-left APP (resp. p.q.-Baer) rings and we show that R is left APP (resp. p.q.-Baer) if and only if for each derivation δ of R, R is δ-weakly rigid and δ-left APP (resp. p.q.-Baer). Finally we prove that R[x;δ] is left APP (resp. p.q.-Baer) if and only if R is δ-left APP (resp. p.q.-Baer). |
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Keywords: | Differential polynomial ring left APP ring left p.q.-Baer ring weakly rigid ring |
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