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On skew power series over McCoy rings | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 19-27 اصل مقاله (511.78 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19231.1227 | ||
| نویسندگان | ||
| Masoome Zahiri* ؛ Saeide Zahiri | ||
| Department of Mathematics, Higher Education center of Eghlid, Eghlid, Iran | ||
| چکیده | ||
| Let $R$ be a ring with an endomorphism $\alpha$. A ring $R$ is a skew power series McCoy ring if whenever any non-zero power series $f(x)=\sum_{i=0}^{\infty}a_ix^i,g(x)=\sum_{j=0}^{\infty}b_jx^j\in R[[x;\alpha]]$ satisfy $f(x)g(x)=0$, then there exists a non-zero element $c\in R$ such that $a_ic=0$, for all $i=0,1,\ldots$. We investigate relations between the skew power series ring and the standard ring-theoretic properties. Moreover, we obtain some characterizations for skew power series ring $R[[x;\alpha]]$, to be McCoy, zip, strongly \textit{AB} and has Property (A). | ||
| کلیدواژه‌ها | ||
| Noetherian ring؛ $alpha$-compatible ring؛ Skew Power series McCoy ring؛ Zip ring؛ Reversible ring | ||
| مراجع | ||
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[7] E. Hashemi, A. As. Estaji and M. Ziembowski, Answers to some questions concerning rings with Property (A) Proc. Edinb. Math. Soc., in prees.
[8] T.K. Kwak and Y. Lee, Zero divisors in skew power series rings, Comm. Algebra., 43, No 10(2015), 4427{4445.
[9] T.Y. Lam, A First Course in Noncommutative Rings, Second edition. Graduate Texts in Mathematics, 131. Springer-Verlag, New York, 2001. | ||
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