Research Article
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Year 2019, , 1815 - 1823, 08.12.2019
https://doi.org/10.15672/HJMS.2018.646

Abstract

References

  • [1] S.A. Amitsur, Radicals of polynomial rings, Canad. J. Math. 8, 355–361, 1956.
  • [2] J. Chen, X. Yang, and Y. Zhou, On strongly clean matrix and triangular matrix rings, Comm. Algebra. 34, 3659–3674, 2006.
  • [3] W. Chen, Polynomial rings over weak Armendariz rings need not be weak Armendariz, Comm. Algebra. 42, 2528–2532, 2014.
  • [4] J. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc. 38 (2), 85–88, 1932.
  • [5] M. Habibi and A. Moussavi, Annihilator Properties of Skew Monoid Rings, Comm. Algebra, 42 (2), 842–852, 2014.
  • [6] M. Habibi, A. Moussavi and S. Mokhtari, On skew Armendariz of Laurent series type rings, Comm. Algebra, 40 (11), 3999–4018, 2012.
  • [7] C.Y. Hong, N.K. Kim and T.K. Kwak, Ore extensions of baer and pp-rings, J. Pure Appl. Algebra, 151 (3), 215–226, 2000.
  • [8] C.Y. Hong, N.K. Kim, and T.K. Kwak, On skew Armendariz rings, Comm. Algebra, 31 (1), 2511–2528, 2003.
  • [9] D. Jordan, Bijective extensions of injective ring endomorphisms, J. Lond. Math. Soc. 2 (3), 435–448, 1982.
  • [10] J. Krempa, Some examples of reduced rings, Algebra Colloq. 3, 289–300, 1996.
  • [11] J. Matczuk, A characterization of σ-rigid rings, Comm. Algebra, 32 (11), 4333–4336, 2004.
  • [12] K. Paykan and M. Habibi, Further results on Skew Monoid Rings of a certain free monoid, Cogent Math. Stat. 5 (1), 1–12, 2018.
  • [13] M. Sanaei, S. Sahebi, and H.H. Javadi, $\alpha$-skew $J$-Armendariz rings, J. Math. Ext. 12 (1), 63–72, 2018.

On $J$-rigid rings

Year 2019, , 1815 - 1823, 08.12.2019
https://doi.org/10.15672/HJMS.2018.646

Abstract

Let $R$ be a ring with an endomorphism $\sigma$. We introduce the notion of $\sigma$-$J$-rigid rings as a generalization of $\sigma$-rigid rings, and investigate its properties. It is proved that a ring $R$ is $\sigma$-$J$-rigid if and only if $R[[x;\sigma]]$ is $\bar\sigma$-$J$-rigid, while the $\sigma$-$J$-rigid property is not Morita invariant. Moreover, we prove that every ring isomorphism preserves $J$-rigid structure, and several known results are extended.

References

  • [1] S.A. Amitsur, Radicals of polynomial rings, Canad. J. Math. 8, 355–361, 1956.
  • [2] J. Chen, X. Yang, and Y. Zhou, On strongly clean matrix and triangular matrix rings, Comm. Algebra. 34, 3659–3674, 2006.
  • [3] W. Chen, Polynomial rings over weak Armendariz rings need not be weak Armendariz, Comm. Algebra. 42, 2528–2532, 2014.
  • [4] J. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc. 38 (2), 85–88, 1932.
  • [5] M. Habibi and A. Moussavi, Annihilator Properties of Skew Monoid Rings, Comm. Algebra, 42 (2), 842–852, 2014.
  • [6] M. Habibi, A. Moussavi and S. Mokhtari, On skew Armendariz of Laurent series type rings, Comm. Algebra, 40 (11), 3999–4018, 2012.
  • [7] C.Y. Hong, N.K. Kim and T.K. Kwak, Ore extensions of baer and pp-rings, J. Pure Appl. Algebra, 151 (3), 215–226, 2000.
  • [8] C.Y. Hong, N.K. Kim, and T.K. Kwak, On skew Armendariz rings, Comm. Algebra, 31 (1), 2511–2528, 2003.
  • [9] D. Jordan, Bijective extensions of injective ring endomorphisms, J. Lond. Math. Soc. 2 (3), 435–448, 1982.
  • [10] J. Krempa, Some examples of reduced rings, Algebra Colloq. 3, 289–300, 1996.
  • [11] J. Matczuk, A characterization of σ-rigid rings, Comm. Algebra, 32 (11), 4333–4336, 2004.
  • [12] K. Paykan and M. Habibi, Further results on Skew Monoid Rings of a certain free monoid, Cogent Math. Stat. 5 (1), 1–12, 2018.
  • [13] M. Sanaei, S. Sahebi, and H.H. Javadi, $\alpha$-skew $J$-Armendariz rings, J. Math. Ext. 12 (1), 63–72, 2018.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Soraya Karimi This is me 0000-0002-5690-4602

Shervin Sahebi 0000-0003-0114-8798

Mohammad Habibi This is me 0000-0003-1317-1434

Publication Date December 8, 2019
Published in Issue Year 2019

Cite

APA Karimi, S., Sahebi, S., & Habibi, M. (2019). On $J$-rigid rings. Hacettepe Journal of Mathematics and Statistics, 48(6), 1815-1823. https://doi.org/10.15672/HJMS.2018.646
AMA Karimi S, Sahebi S, Habibi M. On $J$-rigid rings. Hacettepe Journal of Mathematics and Statistics. December 2019;48(6):1815-1823. doi:10.15672/HJMS.2018.646
Chicago Karimi, Soraya, Shervin Sahebi, and Mohammad Habibi. “On $J$-Rigid Rings”. Hacettepe Journal of Mathematics and Statistics 48, no. 6 (December 2019): 1815-23. https://doi.org/10.15672/HJMS.2018.646.
EndNote Karimi S, Sahebi S, Habibi M (December 1, 2019) On $J$-rigid rings. Hacettepe Journal of Mathematics and Statistics 48 6 1815–1823.
IEEE S. Karimi, S. Sahebi, and M. Habibi, “On $J$-rigid rings”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, pp. 1815–1823, 2019, doi: 10.15672/HJMS.2018.646.
ISNAD Karimi, Soraya et al. “On $J$-Rigid Rings”. Hacettepe Journal of Mathematics and Statistics 48/6 (December 2019), 1815-1823. https://doi.org/10.15672/HJMS.2018.646.
JAMA Karimi S, Sahebi S, Habibi M. On $J$-rigid rings. Hacettepe Journal of Mathematics and Statistics. 2019;48:1815–1823.
MLA Karimi, Soraya et al. “On $J$-Rigid Rings”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, 2019, pp. 1815-23, doi:10.15672/HJMS.2018.646.
Vancouver Karimi S, Sahebi S, Habibi M. On $J$-rigid rings. Hacettepe Journal of Mathematics and Statistics. 2019;48(6):1815-23.