Annihilator condition does not pass to polynomials and power series

Grzegorz Bajor , Michał Ziembowski

Abstract

In this paper we construct a ring A which has annihilator condition (a.c.) and we show that neither A[x] nor A[[x]] has this property. This answers in negative a question asked by Hong, Kim, Lee and Nielsen. We also show that there is an algebra A which does not have annihilator condition while both A[x] and A[[x]] have this property.
Author Grzegorz Bajor (FMIS)
Grzegorz Bajor,,
- Faculty of Mathematics and Information Science
, Michał Ziembowski (FMIS / DAC)
Michał Ziembowski,,
- Department of Algebra and Combinatorics
Journal seriesJournal of Pure and Applied Algebra, ISSN 0022-4049, (A 25 pkt)
Issue year2019
Vol223
No9
Pages3869-3878
Publication size in sheets0.5
Keywords in Polishwarunki anihilatorowe, anihilatory
Keywords in Englishannihilator condition (a.c.), annihilators
ASJC Classification2602 Algebra and Number Theory
Abstract in PolishW pracy został skonstruowany pierścień A z warunkiem anihilatorowym (a.c.), taki że A[x] i A[[x]] nie spełniają tej własności. Podobnie została pokazana algebra A nie spełniająca warunku anihilatorowego, natomiast A[x] i A[[x]] spełniają tę własność
DOIDOI:10.1016/j.jpaa.2018.12.009
URL https://www.sciencedirect.com/science/article/pii/S0022404918302998
Languageen angielski
Score (nominal)25
ScoreMinisterial score = 25.0, 08-07-2019, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2016 = 1.159; WoS Impact Factor: 2017 = 0.72 (2) - 2017=0.68 (5)
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