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Year 2019, Volume 48, Issue 6, 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, Volume 48, Issue 6, 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.

Details

Primary Language English
Subjects Mathematics
Journal Section Mathematics
Authors

Soraya KARİMİ This is me
Islamic Azad University
0000-0002-5690-4602
Iran


Shervin SAHEBİ (Primary Author)
Islamic Azad University
0000-0003-0114-8798
Iran


Mohammad HABİBİ This is me
Tafresh University
0000-0003-1317-1434
Iran

Publication Date December 8, 2019
Published in Issue Year 2019, Volume 48, Issue 6

Cite

Bibtex @research article { hujms504548, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, pages = {1815 - 1823}, doi = {10.15672/HJMS.2018.646}, title = {On \$J\$-rigid rings}, key = {cite}, author = {Karimi, Soraya and Sahebi, Shervin and Habibi, Mohammad} }
APA Karimi, S. , Sahebi, S. & Habibi, M. (2019). On $J$-rigid rings . Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1815-1823 . DOI: 10.15672/HJMS.2018.646
MLA Karimi, S. , Sahebi, S. , Habibi, M. "On $J$-rigid rings" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1815-1823 <https://dergipark.org.tr/en/pub/hujms/article/504548>
Chicago Karimi, S. , Sahebi, S. , Habibi, M. "On $J$-rigid rings". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1815-1823
RIS TY - JOUR T1 - On $J$-rigid rings AU - Soraya Karimi , Shervin Sahebi , Mohammad Habibi Y1 - 2019 PY - 2019 N1 - doi: 10.15672/HJMS.2018.646 DO - 10.15672/HJMS.2018.646 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1815 EP - 1823 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2018.646 UR - https://doi.org/10.15672/HJMS.2018.646 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On $J$-rigid rings %A Soraya Karimi , Shervin Sahebi , Mohammad Habibi %T On $J$-rigid rings %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R doi: 10.15672/HJMS.2018.646 %U 10.15672/HJMS.2018.646
ISNAD Karimi, Soraya , Sahebi, Shervin , Habibi, Mohammad . "On $J$-rigid rings". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 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. 2019; 48(6): 1815-1823.
Vancouver Karimi S. , Sahebi S. , Habibi M. On $J$-rigid rings. Hacettepe Journal of Mathematics and Statistics. 2019; 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, Dec. 2019, doi:10.15672/HJMS.2018.646