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Quasi-duo differential polynomial rings. (English) Zbl 1385.16021

Summary: In this paper, we give a characterization of left (right) quasi-duo differential polynomial rings. In particular, we show that a differential polynomial ring is left quasi-duo if and only if it is right quasi-duo. This yields a partial answer to a question posed by T. Y. Lam and A. S. Dugas [J. Pure Appl. Algebra 195, No. 3, 243–259 (2005; Zbl 1071.16003)]. We provide nontrivial examples of such rings and give a complete description of the maximal ideals of an arbitrary quasi-duo differential polynomial ring. Moreover, we show that there is no left (right) quasi-duo differential polynomial ring in several indeterminates.

MSC:

16S32 Rings of differential operators (associative algebraic aspects)
16W70 Filtered associative rings; filtrational and graded techniques
16D25 Ideals in associative algebras

Citations:

Zbl 1071.16003
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References:

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