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Year 2021, , 231 - 242, 17.07.2021
https://doi.org/10.24330/ieja.969915

Abstract

References

  • M. Ahmadi, N. Golestani and A. Moussavi, Generalized quasi-Baer $ \ast $-rings and Banach $ \ast $-algebras, Comm. Algebra, 48(5) (2020), 2207-2247.
  • E. P. Armendariz, A note on extensions of Baer and p.p. rings, J. Austral. Math. Soc., 18 (1974), 470-473.
  • H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc., 2 (1973), 363-368.
  • S. K. Berberian, Baer $ \ast $-Rings, Grundlehren Math. Wiss., Vol. 195, Springer-Verlag, New York-Berlin, 1972.
  • G. F. Birkenmeier N. J. Groenewald and H. E. Heatherly, Minimal and maximal ideals in rings with involution, Beitrage Algebra Geom., 38(2) (1997), 217-225.
  • G. F. Birkenmeier, Y. Kara and A. Tercan, $\pi$-Baer rings, J. Algebra Appl., 17(2) (2018), 1850029 (19 pp).
  • G. F. Birkenmeier, J. Y. Kim and J. K. Park, Quasi-Baer ring extensions and biregular rings, Bull. Austral. Math. Soc., 61(1) (2000), 39-52.
  • G. F. Birkenmeier, J. Y. Kim and J. K. Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra, 159(1) (2001), 25-42.
  • G. F. Birkenmeier, B. J. Muller and S. T. Rizvi, Modules in which every fully invariant submodule is essential in a direct summand, Comm. Algebra, 30(3) (2002), 1395-1415.
  • G. F. Birkenmeier and J. K. Park, Self-adjoint ideals in Baer $ \ast $-rings, Comm. Algebra, 28(9) (2000), 4259-4268.
  • G. F. Birkenmeier and J. K. Park, Triangular matrix representations of ring extensions, J. Algebra, 265(2) (2003), 457-477.
  • G. F. Birkenmeier, J. K. Park and S. T. Rizvi, Hulls of semiprime rings withapplications to C*-algebras, J. Algebra, 322(2) (2009), 327-352.
  • G. F. Birkenmeier, J. K. Park and S. T. Rizvi, Extensions of Rings and Modules, Birkhauser/Springer, New York, 2013.
  • K. A. Brown, The singular ideals of group rings, Quart. J. Math. Oxford Ser. (2), 28(109) (1977), 41-60.
  • W. E. Clark, Twisted matrix units semigroup algebras, Duke Math. J., 34 (1967), 417-423.
  • D. E. Handelman, Prufer domains and Baer $ \ast $-rings, Arch. Math. (Basel), 29(3) (1977), 241-251.
  • I. Kaplansky, Rings of Operators, W. A. Benjamin, Inc., New York-Amsterdam, 1968.
  • T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, 189, Springer-Verlag, New York, 1999.
  • W. Narkiewicz, Polynomial Mappings, Lecture Notes in Mathematics, 1600, Springer-Verlag, Berlin, 1995.

$\pi$-BAER $\ast$-RINGS

Year 2021, , 231 - 242, 17.07.2021
https://doi.org/10.24330/ieja.969915

Abstract

A $\ast$-ring
$R$ is called a $\pi$-Baer $\ast$-ring, if for any projection invariant left ideal $Y$ of $R$, the right annihilator of $Y $
is generated, as a right ideal, by a projection.
In this note, we
study some properties of such $\ast$-rings.
We indicate interrelationships between the $\pi$-Baer $\ast$-rings and related classes of rings such as
$\pi$-Baer rings, Baer $\ast$-rings, and quasi-Baer $\ast$-rings. We announce several
results on $\pi$-Baer $\ast$-rings.
We show that this notion is well-behaved with respect to
polynomial extensions and full matrix rings.
Examples are provided to explain and delimit our results.

References

  • M. Ahmadi, N. Golestani and A. Moussavi, Generalized quasi-Baer $ \ast $-rings and Banach $ \ast $-algebras, Comm. Algebra, 48(5) (2020), 2207-2247.
  • E. P. Armendariz, A note on extensions of Baer and p.p. rings, J. Austral. Math. Soc., 18 (1974), 470-473.
  • H. E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc., 2 (1973), 363-368.
  • S. K. Berberian, Baer $ \ast $-Rings, Grundlehren Math. Wiss., Vol. 195, Springer-Verlag, New York-Berlin, 1972.
  • G. F. Birkenmeier N. J. Groenewald and H. E. Heatherly, Minimal and maximal ideals in rings with involution, Beitrage Algebra Geom., 38(2) (1997), 217-225.
  • G. F. Birkenmeier, Y. Kara and A. Tercan, $\pi$-Baer rings, J. Algebra Appl., 17(2) (2018), 1850029 (19 pp).
  • G. F. Birkenmeier, J. Y. Kim and J. K. Park, Quasi-Baer ring extensions and biregular rings, Bull. Austral. Math. Soc., 61(1) (2000), 39-52.
  • G. F. Birkenmeier, J. Y. Kim and J. K. Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra, 159(1) (2001), 25-42.
  • G. F. Birkenmeier, B. J. Muller and S. T. Rizvi, Modules in which every fully invariant submodule is essential in a direct summand, Comm. Algebra, 30(3) (2002), 1395-1415.
  • G. F. Birkenmeier and J. K. Park, Self-adjoint ideals in Baer $ \ast $-rings, Comm. Algebra, 28(9) (2000), 4259-4268.
  • G. F. Birkenmeier and J. K. Park, Triangular matrix representations of ring extensions, J. Algebra, 265(2) (2003), 457-477.
  • G. F. Birkenmeier, J. K. Park and S. T. Rizvi, Hulls of semiprime rings withapplications to C*-algebras, J. Algebra, 322(2) (2009), 327-352.
  • G. F. Birkenmeier, J. K. Park and S. T. Rizvi, Extensions of Rings and Modules, Birkhauser/Springer, New York, 2013.
  • K. A. Brown, The singular ideals of group rings, Quart. J. Math. Oxford Ser. (2), 28(109) (1977), 41-60.
  • W. E. Clark, Twisted matrix units semigroup algebras, Duke Math. J., 34 (1967), 417-423.
  • D. E. Handelman, Prufer domains and Baer $ \ast $-rings, Arch. Math. (Basel), 29(3) (1977), 241-251.
  • I. Kaplansky, Rings of Operators, W. A. Benjamin, Inc., New York-Amsterdam, 1968.
  • T. Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, 189, Springer-Verlag, New York, 1999.
  • W. Narkiewicz, Polynomial Mappings, Lecture Notes in Mathematics, 1600, Springer-Verlag, Berlin, 1995.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ali Shahıdıkıa This is me

Hamid Haj Seyyed Javadı This is me

Ahmad Moussavı This is me

Publication Date July 17, 2021
Published in Issue Year 2021

Cite

APA Shahıdıkıa, A., Javadı, H. H. S., & Moussavı, A. (2021). $\pi$-BAER $\ast$-RINGS. International Electronic Journal of Algebra, 30(30), 231-242. https://doi.org/10.24330/ieja.969915
AMA Shahıdıkıa A, Javadı HHS, Moussavı A. $\pi$-BAER $\ast$-RINGS. IEJA. July 2021;30(30):231-242. doi:10.24330/ieja.969915
Chicago Shahıdıkıa, Ali, Hamid Haj Seyyed Javadı, and Ahmad Moussavı. “$\pi$-BAER $\ast$-RINGS”. International Electronic Journal of Algebra 30, no. 30 (July 2021): 231-42. https://doi.org/10.24330/ieja.969915.
EndNote Shahıdıkıa A, Javadı HHS, Moussavı A (July 1, 2021) $\pi$-BAER $\ast$-RINGS. International Electronic Journal of Algebra 30 30 231–242.
IEEE A. Shahıdıkıa, H. H. S. Javadı, and A. Moussavı, “$\pi$-BAER $\ast$-RINGS”, IEJA, vol. 30, no. 30, pp. 231–242, 2021, doi: 10.24330/ieja.969915.
ISNAD Shahıdıkıa, Ali et al. “$\pi$-BAER $\ast$-RINGS”. International Electronic Journal of Algebra 30/30 (July 2021), 231-242. https://doi.org/10.24330/ieja.969915.
JAMA Shahıdıkıa A, Javadı HHS, Moussavı A. $\pi$-BAER $\ast$-RINGS. IEJA. 2021;30:231–242.
MLA Shahıdıkıa, Ali et al. “$\pi$-BAER $\ast$-RINGS”. International Electronic Journal of Algebra, vol. 30, no. 30, 2021, pp. 231-42, doi:10.24330/ieja.969915.
Vancouver Shahıdıkıa A, Javadı HHS, Moussavı A. $\pi$-BAER $\ast$-RINGS. IEJA. 2021;30(30):231-42.