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22 p, 386.3 KB Five solved problems on radicals of ore extensions / Greenfeld, Be'eri (Bar Ilan University (Israel). Department of Mathematics) ; Smoktunowicz, Agata (University of Edinburgh. School of Mathematics) ; Ziembowski, Michal (Warsaw University of Technology (Polònia). Faculty of Mathematics and Information Science)
We answer several open questions and establish new results concerningdierential and skew polynomial ring extensions, with emphasis on radicals. In particular, we prove the following results. If R is prime radical and δ is a derivation of R, then the dierential polynomial ring R[X; δ] is locally nilpotent. [...]
2019 - 10.5565/PUBLMAT6321902
Publicacions matemàtiques, Vol. 63 Núm. 2 (2019) , p. 423-444 (Articles)  
15 p, 153.9 KB Duo, Bézout and distributive rings of skew power series / Mazurek, Ryszard (Bialystok Technical University (Polònia). Faculty of Computer Science) ; Ziembowski, Michal (University of Edinburgh. School of Mathematics)
We give necessary and sufficient conditions on a ring R and an endomorphism σ of R for the skew power series ring R[[x; σ]] to be right duo right Bézout. In particular, we prove that R[[x; σ]] is right duo right Bézout if and only if R[[x; σ]] is reduced right distributive if and only if R[[x; σ]] is right duo of weak dimension less than or equal to 1 if and only if R is N0-injective strongly regular and σ is bijective and idempotent-stabilizing, extending to skew power series rings the Brewer-Rutter-Watkins characterization of commutative B'ezout power series rings.
2009 - 10.5565/PUBLMAT_53209_01
Publicacions matemàtiques, V. 53 n. 2 (2009) p. 257-271  

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2 Ziembowski, Michal
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