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Some results on relative dual Baer property

Yıl 2020, Cilt: 7 Sayı: 3, 259 - 267, 06.09.2020
https://doi.org/10.13069/jacodesmath.790751

Öz

Let $R$ be a ring.
In this article, we introduce and study relative dual Baer property.
We characterize $R$-modules $M$ which are $R_R$-dual Baer, where $R$ is a commutative principal ideal domain.
It is shown that over a right noetherian right hereditary ring $R$, an $R$-module $M$ is $N$-dual Baer for
all $R$-modules $N$ if and only if $M$ is an injective $R$-module.
It is also shown that for $R$-modules $M_1$, $M_2$, $\ldots$, $M_n$ such that $M_i$ is $M_j$-projective for all
$i > j \in \{1,2,\ldots, n\}$, an $R$-module $N$ is $\bigoplus_{i=1}^nM_i$-dual Baer if and only if $N$ is
$M_i$-dual Baer for all $i\in \{1,2,\ldots,n\}$.
We prove that an $R$-module $M$ is dual Baer if and only if $S=End_R(M)$ is a Baer ring
and $IM=r_M(l_S(IM))$ for every right ideal $I$ of $S$.

Kaynakça

  • [1] F. W. Anderson, K. R. Fuller, Rings and Categories of Modules, vol. 13, Springer–Verlag, New York 1992.
  • [2] E. P. Armendariz, A note on extensions of Baer and P.P.–rings, J. Austral. Math. Soc. 18(4) (1974) 470–473.
  • [3] G. F. Birkenmeier, J. Y. Kim, J. K. Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra 159(1) (2001) 25–42.
  • [4] K. A. Byrd, Rings whose quasi-injective modules are injective, Proc. Amer. Math. Soc. 33(2) (1972) 235–240.
  • [5] S. M. Khuri, Baer endomorphism rings and closure operators, Canad. J. Math. 30(5) (1978) 1070– 1078.
  • [6] I. Kaplansky, Rings of Operators, W. A. Benjamin Inc., New York-Amsterdam 1968.
  • [7] G. Lee, S. T. Rizvi, C. S. Roman, Rickart modules, Comm. Algebra 38(11) (2010) 4005–4027.
  • [8] G. Lee, S. T. Rizvi, C. S. Roman, Dual Rickart modules, Comm. Algebra 39(11) (2011) 4036–4058.
  • [9] S. H. Mohamed, B. J. Müller, Continuous and Discrete Modules, London Math. Soc. Lecture Notes Series 147, Cambridge University Press 1990.
  • [10] S. T. Rizvi, C. S. Roman, Baer and quasi-Baer modules, Comm. Algebra 32(1) (2004) 103–123.
  • [11] S. T. Rizvi, C. S. Roman, Baer property of modules and applications, Advances in Ring Theory (2005) 225–241.
  • [12] D. W. Sharpe, P. Vámos, Injective Modules, Cambridge University Press, Cambridge 1972.
  • [13] Y. Talebi, N. Vanaja, The torsion theory cogenerated by M-small modules, Comm. Algebra 30(3) (2002) 1449–1460.
  • [14] D. K. Tütüncü and R. Tribak, On dual Baer modules, Glasgow Math. J. 52(2) (2010) 261–269.
  • [15] D. K. Tütüncü, P. F. Smith, S. E. Toksoy, On dual Baer modules, Contemp. Math. 609 (2014) 173–184.
  • [16] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers, Philadelphia 1991.
Yıl 2020, Cilt: 7 Sayı: 3, 259 - 267, 06.09.2020
https://doi.org/10.13069/jacodesmath.790751

Öz

Kaynakça

  • [1] F. W. Anderson, K. R. Fuller, Rings and Categories of Modules, vol. 13, Springer–Verlag, New York 1992.
  • [2] E. P. Armendariz, A note on extensions of Baer and P.P.–rings, J. Austral. Math. Soc. 18(4) (1974) 470–473.
  • [3] G. F. Birkenmeier, J. Y. Kim, J. K. Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra 159(1) (2001) 25–42.
  • [4] K. A. Byrd, Rings whose quasi-injective modules are injective, Proc. Amer. Math. Soc. 33(2) (1972) 235–240.
  • [5] S. M. Khuri, Baer endomorphism rings and closure operators, Canad. J. Math. 30(5) (1978) 1070– 1078.
  • [6] I. Kaplansky, Rings of Operators, W. A. Benjamin Inc., New York-Amsterdam 1968.
  • [7] G. Lee, S. T. Rizvi, C. S. Roman, Rickart modules, Comm. Algebra 38(11) (2010) 4005–4027.
  • [8] G. Lee, S. T. Rizvi, C. S. Roman, Dual Rickart modules, Comm. Algebra 39(11) (2011) 4036–4058.
  • [9] S. H. Mohamed, B. J. Müller, Continuous and Discrete Modules, London Math. Soc. Lecture Notes Series 147, Cambridge University Press 1990.
  • [10] S. T. Rizvi, C. S. Roman, Baer and quasi-Baer modules, Comm. Algebra 32(1) (2004) 103–123.
  • [11] S. T. Rizvi, C. S. Roman, Baer property of modules and applications, Advances in Ring Theory (2005) 225–241.
  • [12] D. W. Sharpe, P. Vámos, Injective Modules, Cambridge University Press, Cambridge 1972.
  • [13] Y. Talebi, N. Vanaja, The torsion theory cogenerated by M-small modules, Comm. Algebra 30(3) (2002) 1449–1460.
  • [14] D. K. Tütüncü and R. Tribak, On dual Baer modules, Glasgow Math. J. 52(2) (2010) 261–269.
  • [15] D. K. Tütüncü, P. F. Smith, S. E. Toksoy, On dual Baer modules, Contemp. Math. 609 (2014) 173–184.
  • [16] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach Science Publishers, Philadelphia 1991.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Tayyebeh Amouzegar Bu kişi benim 0000-0002-0600-5326

Rachid Tribak 0000-0001-8400-4321

Yayımlanma Tarihi 6 Eylül 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 7 Sayı: 3

Kaynak Göster

APA Amouzegar, T., & Tribak, R. (2020). Some results on relative dual Baer property. Journal of Algebra Combinatorics Discrete Structures and Applications, 7(3), 259-267. https://doi.org/10.13069/jacodesmath.790751
AMA Amouzegar T, Tribak R. Some results on relative dual Baer property. Journal of Algebra Combinatorics Discrete Structures and Applications. Eylül 2020;7(3):259-267. doi:10.13069/jacodesmath.790751
Chicago Amouzegar, Tayyebeh, ve Rachid Tribak. “Some Results on Relative Dual Baer Property”. Journal of Algebra Combinatorics Discrete Structures and Applications 7, sy. 3 (Eylül 2020): 259-67. https://doi.org/10.13069/jacodesmath.790751.
EndNote Amouzegar T, Tribak R (01 Eylül 2020) Some results on relative dual Baer property. Journal of Algebra Combinatorics Discrete Structures and Applications 7 3 259–267.
IEEE T. Amouzegar ve R. Tribak, “Some results on relative dual Baer property”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 7, sy. 3, ss. 259–267, 2020, doi: 10.13069/jacodesmath.790751.
ISNAD Amouzegar, Tayyebeh - Tribak, Rachid. “Some Results on Relative Dual Baer Property”. Journal of Algebra Combinatorics Discrete Structures and Applications 7/3 (Eylül 2020), 259-267. https://doi.org/10.13069/jacodesmath.790751.
JAMA Amouzegar T, Tribak R. Some results on relative dual Baer property. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020;7:259–267.
MLA Amouzegar, Tayyebeh ve Rachid Tribak. “Some Results on Relative Dual Baer Property”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 7, sy. 3, 2020, ss. 259-67, doi:10.13069/jacodesmath.790751.
Vancouver Amouzegar T, Tribak R. Some results on relative dual Baer property. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020;7(3):259-67.