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Formal Power Series Over Strongly Hopfian RingsCommunications in Algebra, 39
- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Malaysian Mathematical Sciences Society and Universiti Sains Malaysia
- Subject
- Mathematics; Mathematics, general; Applications of Mathematics
- ISSN
- 0126-6705
- eISSN
- 2180-4206
- DOI
- 10.1007/s40840-015-0298-7
- Publisher site
- See Article on Publisher Site
Abstract
An associative ring is said to be right strongly Hopfian if the chain of right annihilators $$r_R(a)\subseteq r_R(a^2)\subseteq \cdots $$ r R ( a ) ⊆ r R ( a 2 ) ⊆ ⋯ stabilizes for each $$a\in R$$ a ∈ R . In this article, we are interested in the class of right strongly Hopfian rings and the transfer of this property from an associative ring R to the Ore extension $$R[x;\alpha ,\delta ]$$ R [ x ; α , δ ] and the monoid ring R[M]. It is proved that if R is $$(\alpha ,\delta )$$ ( α , δ ) -compatible and $$R[x;\alpha ,\delta ]$$ R [ x ; α , δ ] is reversible, then the Ore extension $$R[x;\alpha ,\delta ]$$ R [ x ; α , δ ] is right strongly Hopfian if and only if R is right strongly Hopfian, and it is also shown that if M is a strictly totally ordered monoid and R[M] is a reversible ring, then the monoid ring R[M] is right strongly Hopfian if and only if R is right strongly Hopfian. Consequently, several known results regarding strongly Hopfian rings are extended to a more general setting.
Journal
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: Feb 1, 2016