On weakened ( α , δ ) -skew Armendariz rings

Alireza Majdabadi Farahani; Mohammad Maghasedi; Farideh Heydari; Hamidagha Tavallaee

Mathematica Bohemica (2022)

  • Volume: 147, Issue: 2, page 187-200
  • ISSN: 0862-7959

Abstract

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In this note, for a ring endomorphism α and an α -derivation δ of a ring R , the notion of weakened ( α , δ ) -skew Armendariz rings is introduced as a generalization of α -rigid rings and weak Armendariz rings. It is proved that R is a weakened ( α , δ ) -skew Armendariz ring if and only if T n ( R ) is weakened ( α ¯ , δ ¯ ) -skew Armendariz if and only if R [ x ] / ( x n ) is weakened ( α ¯ , δ ¯ ) -skew Armendariz ring for any positive integer n .

How to cite

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Farahani, Alireza Majdabadi, et al. "On weakened $(\alpha ,\delta )$-skew Armendariz rings." Mathematica Bohemica 147.2 (2022): 187-200. <http://eudml.org/doc/297918>.

@article{Farahani2022,
abstract = {In this note, for a ring endomorphism $\alpha $ and an $\alpha $-derivation $\delta $ of a ring $R$, the notion of weakened $(\alpha ,\delta )$-skew Armendariz rings is introduced as a generalization of $\alpha $-rigid rings and weak Armendariz rings. It is proved that $R$ is a weakened $(\alpha ,\delta )$-skew Armendariz ring if and only if $T_n(R)$ is weakened $(\bar\{\alpha \},\bar\{\delta \})$-skew Armendariz if and only if $R[x]/(x^n)$ is weakened $(\bar\{\alpha \},\bar\{\delta \})$-skew Armendariz ring for any positive integer $n$.},
author = {Farahani, Alireza Majdabadi, Maghasedi, Mohammad, Heydari, Farideh, Tavallaee, Hamidagha},
journal = {Mathematica Bohemica},
keywords = {Armendariz ring; $(\alpha ,\delta )$-skew Armendariz ring; weak Armendariz ring; weak $(\alpha ,\delta )$-skew Armendariz ring},
language = {eng},
number = {2},
pages = {187-200},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On weakened $(\alpha ,\delta )$-skew Armendariz rings},
url = {http://eudml.org/doc/297918},
volume = {147},
year = {2022},
}

TY - JOUR
AU - Farahani, Alireza Majdabadi
AU - Maghasedi, Mohammad
AU - Heydari, Farideh
AU - Tavallaee, Hamidagha
TI - On weakened $(\alpha ,\delta )$-skew Armendariz rings
JO - Mathematica Bohemica
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 147
IS - 2
SP - 187
EP - 200
AB - In this note, for a ring endomorphism $\alpha $ and an $\alpha $-derivation $\delta $ of a ring $R$, the notion of weakened $(\alpha ,\delta )$-skew Armendariz rings is introduced as a generalization of $\alpha $-rigid rings and weak Armendariz rings. It is proved that $R$ is a weakened $(\alpha ,\delta )$-skew Armendariz ring if and only if $T_n(R)$ is weakened $(\bar{\alpha },\bar{\delta })$-skew Armendariz if and only if $R[x]/(x^n)$ is weakened $(\bar{\alpha },\bar{\delta })$-skew Armendariz ring for any positive integer $n$.
LA - eng
KW - Armendariz ring; $(\alpha ,\delta )$-skew Armendariz ring; weak Armendariz ring; weak $(\alpha ,\delta )$-skew Armendariz ring
UR - http://eudml.org/doc/297918
ER -

References

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  1. Alhevaz, A., Moussavi, A., Habibi, M., 10.1080/00927872.2010.548842, Commun. Algebra 40 (2012), 1195-1221. (2012) Zbl1260.16024MR2912979DOI10.1080/00927872.2010.548842
  2. Anderson, D. D., Camillo, V., 10.1080/00927879808826274, Commun. Algebra 26 (1998), 2265-2272. (1998) Zbl0915.13001MR1626606DOI10.1080/00927879808826274
  3. Anderson, D. D., Camillo, V., 10.1080/00927879908826596, Commun. Algebra 27 (1999), 2847-2852. (1999) Zbl0929.16032MR1687281DOI10.1080/00927879908826596
  4. Annin, S., 10.1081/AGB-120003481, Commun. Algebra 30 (2002), 2511-2528. (2002) Zbl1010.16025MR1904650DOI10.1081/AGB-120003481
  5. Armendariz, E. P., 10.1017/S1446788700029190, J. Aust. Math. Soc. 18 (1974), 470-473. (1974) Zbl0292.16009MR0366979DOI10.1017/S1446788700029190
  6. Chen, J., Yang, X., Zhou, Y., 10.1080/00927870600860791, Commun. Algebra 34 (2006), 3659-3674. (2006) Zbl1114.16024MR2262376DOI10.1080/00927870600860791
  7. Chen, J., Zhou, Y., 10.1080/00927870500346263, Commun. Algebra 34 (2006), 275-288. (2006) Zbl1112.16002MR2194766DOI10.1080/00927870500346263
  8. Chen, W., Cui, S., On weakly semicommutative rings, Commun. Math. Res. 27 (2011), 179-192. (2011) Zbl1249.16041MR2808276
  9. Habibi, M., Moussavi, A., 10.1142/S1793557112500179, Asian-Eur. J. Math. 5 (2012), Article ID 1250017, 16 pages. (2012) Zbl1263.16028MR2959844DOI10.1142/S1793557112500179
  10. Hashemi, E., Moussavi, A., 10.1007/s10474-005-0191-1, Acta. Math. Hung. 107 (2005), 207-224. (2005) Zbl1081.16032MR2148584DOI10.1007/s10474-005-0191-1
  11. Hirano, Y., On the uniqueness of rings of coefficients in skew polynomial rings, Publ. Math. 54 (1999), 489-495. (1999) Zbl0930.16018MR1694531
  12. Hong, C. Y., Kim, H. K., Kim, N. K., Kwak, T. K., Lee, Y., Park, K. S., 10.1080/00927870601117597, Commun. Algebra 35 (2007), 1379-1390. (2007) Zbl1121.16021MR2313674DOI10.1080/00927870601117597
  13. Hong, C. Y., Kim, N. K., Kwak, T. K., 10.1016/S0022-4049(99)00020-1, J. Pure Appl. Algebra 151 (2000), 215-226. (2000) Zbl0982.16021MR1776431DOI10.1016/S0022-4049(99)00020-1
  14. Huh, C., Lee, Y., Smoktunowicz, A., 10.1081/AGB-120013179, Commun. Algebra 30 (2002), 751-761. (2002) Zbl1023.16005MR1883022DOI10.1081/AGB-120013179
  15. Kim, N. K., Lee, Y., 10.1006/jabr.1999.8017, J. Algebra 223 (2000), 477-488. (2000) Zbl0957.16018MR1735157DOI10.1006/jabr.1999.8017
  16. Kim, N. K., Lee, Y., 10.1016/S0022-4049(03)00109-9, J. Pure Appl. Algebra 185 (2003), 207-223. (2003) Zbl1040.16021MR2006427DOI10.1016/S0022-4049(03)00109-9
  17. Krempa, J., Some examples of reduced rings, Algebra Colloq. 3 (1996), 289-300. (1996) Zbl0859.16019MR1422968
  18. Lam, T. Y., Leroy, A., Matczuk, J., 10.1080/00927879708826000, Commun. Algebra 25 (1997), 2459-2506. (1997) Zbl0879.16016MR1459571DOI10.1080/00927879708826000
  19. Lambek, J., 10.4153/CMB-1971-065-1, Can. Math. Bull. 14 (1971), 359-368. (1971) Zbl0217.34005MR0313324DOI10.4153/CMB-1971-065-1
  20. Liu, Z., Zhao, R., 10.1080/00927870600651398, Commun. Algebra 34 (2006), 2607-2616. (2006) Zbl1110.16026MR2240395DOI10.1080/00927870600651398
  21. Moussavi, A., Hashemi, E., 10.4134/JKMS.2005.42.2.353, J. Korean Math. Soc. 42 (2005), 353-363. (2005) Zbl1090.16012MR2121504DOI10.4134/JKMS.2005.42.2.353
  22. Rege, M. B., Chhawchharia, S., 10.3792/pjaa.73.14, Proc. Japan Acad., Ser. A 73 (1997), 14-17. (1997) Zbl0960.16038MR1442245DOI10.3792/pjaa.73.14
  23. Shin, G., 10.1090/S0002-9947-1973-0338058-9, Trans. Am. Math. Soc. 184 (1973), 43-60. (1973) Zbl0283.16021MR0338058DOI10.1090/S0002-9947-1973-0338058-9
  24. Wang, Y., Jiang, M., Ren, Y., 10.13447/j.1674-5647.2016.01.05, Commun. Math. Res. 32 (2016), 70-82. (2016) Zbl1363.16075MR3467810DOI10.13447/j.1674-5647.2016.01.05

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