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- Title
On Ore extension and skew power series rings with some restrictions on zero-divisors.
- Authors
Hashemi, E.; As. Estaji, A.; Alhevaz, A.
- Abstract
The study of rings with right Property (), has done an important role in noncommutative ring theory. Following literature, a ring has right Property () if every finitely generated two-sided ideal consisting entirely of left zero-divisors has a nonzero right annihilator. Our results in this paper concerns the right Property () of Ore extensions as well as skew power series rings. We will show that if is a right duo ring, then the skew power series ring has right Property (), when is right Noetherian and -compatible. Moreover, for a right duo ring which is -compatible, it is shown that (i) the Ore extension ring has right Property () and (ii) is right zip if and only if is right zip. As a corollary of our results, we provide answers to some open questions related to Property , raised in [C. Y. Hong, N. K. Kim, Y. Lee and S. J. Ryu, Rings with Property () and their extensions, J. Algebra 315 (2007) 612-628].
- Subjects
POWER series rings; SMALL divisors; NONCOMMUTATIVE algebras; NOETHERIAN rings; POLYNOMIAL rings
- Publication
Journal of Algebra & Its Applications, 2017, Vol 16, Issue 9, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S021949881750164X