Annihilator condition does not pass to polynomials and power series

Grzegorz Bajor , Michał Ziembowski


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, (N/A 100 pkt)
Issue year2019
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
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 20-10-2019, ArticleFromJournal
Publication indicators Scopus Citations = 0; WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 1.159; WoS Impact Factor: 2017 = 0.72 (2) - 2017=0.68 (5)
Citation count*
Share Share

Get link to the record

* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
Are you sure?