Article
Full entry | Fulltext not available
(moving wall
24 months)
Feedback
Keywords:
Ore extension; skew McCoy ring; right duo ring; compatibility; Jacobson radical; group ring
Ore extension; skew McCoy ring; right duo ring; compatibility; Jacobson radical; group ring
Summary:
This paper concerns the McCoy property in the context of Ore extensions. We show that if $R$ is a $(\sigma ,\delta )$-compatible Artinian and reversible ring, then the Jacobson radical $J(R)$ is $(\sigma , \delta )$-skew McCoy and that if $R$ is a $(\sigma ,\delta )$-compatible local Artinian and right duo ring, then $J(R)$ is also $(\sigma ,\delta )$-skew McCoy.
References:
[1] Annin, S.: Associated primes over skew polynomial rings. Commun. Algebra 30 (2002), 2511-2528. DOI 10.1081/AGB-120003481 | MR 1904650 | Zbl 1010.16025
[2] Baeck, J., Kim, N. K., Lee, Y., Nielsen, P. P.: Zero-divisor placement, a condition of Camillo, and the McCoy property. J. Pure Appl. Algebra 224 (2020), Article ID 106432, 13 pages. DOI 10.1016/j.jpaa.2020.106432 | MR 4099920 | Zbl 1465.16037
[3] Başer, M., Kwak, T. K., Lee, Y.: The McCoy condition on skew polynomial rings. Commun. Algebra 37 (2009), 4026-4037. DOI 10.1080/00927870802545661 | MR 2573233 | Zbl 1187.16027
[4] Camillo, V., Nielsen, P. P.: McCoy rings and zero-divisors. J. Pure Appl. Algebra 212 (2008), 599-615. DOI 10.1016/j.jpaa.2007.06.010 | MR 2365335 | Zbl 1162.16021
[5] Gutan, M., Kisielewicz, A.: Reversible group rings. J. Algebra 279 (2004), 280-291. DOI 10.1016/j.jalgebra.2004.02.011 | MR 2078399 | Zbl 1068.16033
[6] Habibi, M., Moussavi, A., Alhevaz, A.: The McCoy condition on Ore extensions. Commun. Algebra 41 (2013), 124-141. DOI 10.1080/00927872.2011.623289 | MR 3010526 | Zbl 1269.16019
[7] Hashemi, E., Moussavi, A.: Polynomial extensions of quasi-Baer rings. Acta Math. Hung. 107 (2005), 207-224. DOI 10.1007/s10474-005-0191-1 | MR 2148584 | Zbl 1081.16032
[8] Kaplansky, I.: Fields and Rings. University of Chicago Press, Chicago (1969). MR 0269449 | Zbl 0238.16001
[9] Khurana, A., Khurana, D.: Annihilators of polynomials. Commun. Algebra 48 (2020), 57-62. DOI 10.1080/00927872.2019.1632328 | MR 4060010 | Zbl 1480.16066
[10] Koşan, M. T.: Extensions of rings having McCoy condition. Can. Math. Bull. 52 (2009), 267-272. DOI 10.4153/CMB-2009-029-5 | MR 2512315 | Zbl 1189.16031
[11] Kwak, T. K., Lee, Y.: Rings over which coefficients of nilpotent polynomials are nilpotent. Int. J. Algebra Comput. 21 (2011), 745-762. DOI 10.1142/S0218196711006431 | MR 2827201 | Zbl 1233.16031
[12] Lee, K. S.: Skew McCoy rings and $\sigma$-compatibility. J. Algebra Appl. 23 (2024), Article ID 2450031, 13 pages. DOI 10.1142/S0219498824500312 | MR 4688798 | Zbl 1537.16033
[13] Lei, Z., Chen, J., Ying, Z.: A question on McCoy rings. Bull. Aust. Math. Soc. 76 (2007), 137-141. DOI 10.1017/S0004972700039526 | MR 2343444 | Zbl 1127.16027
[14] Marks, G.: A taxonomy of 2-primal rings. J. Algebra 266 (2003), 494-520. DOI 10.1016/S0021-8693(03)00301-6 | MR 1995125 | Zbl 1045.16001
[15] McCoy, N. H.: Remarks on divisors of zero. Am. Math. Mon. 49 (1942), 286-295. DOI 10.1080/00029890.1942.11991226 | MR 0006150 | Zbl 0060.07703
[16] McLaughlin, J. E.: A note on regular group rings. Mich. Math. J. 5 (1958), 127-128. DOI 10.1307/mmj/1028998056 | MR 0103204 | Zbl 0085.02103
[17] Nielsen, P. P.: Semi-commutativity and the McCoy condition. J. Algebra 298 (2006), 134-141. DOI 10.1016/j.jalgebra.2005.10.008 | MR 2215121 | Zbl 1110.16036
Search
Partner of
