On partial skew Armendariz rings
In this paper we consider rings R with a partial action α of an infinite cyclic group G on R. We introduce the concept of partial skew Armendariz rings and partial α-rigid rings. We show that partial α-rigid rings are partial skew Armendariz rings and we give necessary and sufficient conditions f...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2011 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2011
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154760 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On partial skew Armendariz rings / W. Cortes // Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 1. — С. 23–45. — Бібліогр.: 39 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | In this paper we consider rings R with a partial action α of an infinite cyclic group G on R. We introduce the concept of partial skew Armendariz rings and partial α-rigid rings. We show that partial α-rigid rings are partial skew Armendariz rings and we give necessary and sufficient conditions for R to be a partial skew Armendariz ring. We study the transfer of Baer property, a.c.c. on right annhilators property, right p.p. property and right zip property between R and R[x;α].
We also show that R[x;α] and R⟨x;α⟩ are not necessarily associative rings when R satisfies the concepts mentioned above.
|
|---|---|
| ISSN: | 1726-3255 |