Research Article
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ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS

Year 2019, Volume: 26 Issue: 26 , 131 - 144 , 11.07.2019
https://doi.org/10.24330/ieja.587018
https://izlik.org/JA56ZS48SA

Abstract

In this paper, we give a general method of the construction of a
3-dimensional associative algebra R over an arbitrary field F that is a sum of
two subalgebras R_1 and R_2 (i.e. R = R_1 + R_2).

References

  • K. I. Beidar and A. V. Mikhalev, Generalized polynomial identities and rings that are sums of two subrings, Algebra i Logika, 34(1) (1995), 3-11.
  • L. A. Bokut, Imbeddings into simple associative algebras, Algebra i Logika, 15(2) (1976), 117-142.
  • B. Felzenszwalb, A. Giambruno and G. Leal, On rings which are sums of two PI-subrings: a combinatorial approach, Paci c J. Math., 209(1) (2003), 17-30.
  • O. H. Kegel, Zur Nilpotenz gewisser assoziativer Ringe, Math. Ann., 149 (1962/63), 258-260.
  • O. H. Kegel, On rings that are sums of two subrings, J. Algebra, 1 (1964), 103-109.
  • A. V. Kelarev, A sum of two locally nilpotent rings may be not nil, Arch. Math. (Basel), 60 (1993), 431-435.
  • M. Kepczyk, Note on algebras which are sums of two PI subalgebras, J. Algebra Appl., 14 (2015), 1550149 (10 pp).
  • M. Kepczyk, A note on algebras that are sums of two subalgebras, Canad. Math. Bull., 59 (2016), 340-345.
  • M. Kepczyk, A ring which is a sum of two PI subrings is always a PI ring, Israel J. Math., 221(1) (2017), 481-487.
  • M. Kepczyk and E. R. Puczylowski, On radicals of rings which are sums of two subrings, Arc. Math. (Basel), 66(1) (1996), 8-12.
  • M. Kepczyk and E. R. Puczylowski, Rings which are sums of two subrings, Ring Theory (Miskolc, 1996), J. Pure App. Algebra, 133(1-2) (1998), 151-162.
  • M. Kepczyk and E. R. Puczylowski, Rings which are sums of two subrings satisfying polynomial identities, Comm. Algebra, 29(5) (2001), 2059-2065.
  • M. Kepczyk and E. R. Puczylowski, On the structure of rings which are sums of two subrings, Arc. Math. (Basel), 83(5) (2004), 429-436.
  • G. Kothe, Die Struktur der Ringe, deren Restklassenring nach dem Radikal vollstanding irreduzibel ist., Math. Z., 32 (1930), 161-186.
  • A. Smoktunowicz, On some results related to Kothe's conjecture, Serdica Math. J., 27 (2001), 159-170.
  • A. Smoktunowicz, A simple nil ring exists, Comm. Algebra, 30(1) (2002), 27- 59.
  • B. Stenstrom, Rings of Quotients: Die Grundlehren der Mathematischen Wissenschaften, Band 217, An introduction to methods of ring theory, Springer- Verlag, New York-Heidelberg, 1975.

Year 2019, Volume: 26 Issue: 26 , 131 - 144 , 11.07.2019
https://doi.org/10.24330/ieja.587018
https://izlik.org/JA56ZS48SA

Abstract

References

  • K. I. Beidar and A. V. Mikhalev, Generalized polynomial identities and rings that are sums of two subrings, Algebra i Logika, 34(1) (1995), 3-11.
  • L. A. Bokut, Imbeddings into simple associative algebras, Algebra i Logika, 15(2) (1976), 117-142.
  • B. Felzenszwalb, A. Giambruno and G. Leal, On rings which are sums of two PI-subrings: a combinatorial approach, Paci c J. Math., 209(1) (2003), 17-30.
  • O. H. Kegel, Zur Nilpotenz gewisser assoziativer Ringe, Math. Ann., 149 (1962/63), 258-260.
  • O. H. Kegel, On rings that are sums of two subrings, J. Algebra, 1 (1964), 103-109.
  • A. V. Kelarev, A sum of two locally nilpotent rings may be not nil, Arch. Math. (Basel), 60 (1993), 431-435.
  • M. Kepczyk, Note on algebras which are sums of two PI subalgebras, J. Algebra Appl., 14 (2015), 1550149 (10 pp).
  • M. Kepczyk, A note on algebras that are sums of two subalgebras, Canad. Math. Bull., 59 (2016), 340-345.
  • M. Kepczyk, A ring which is a sum of two PI subrings is always a PI ring, Israel J. Math., 221(1) (2017), 481-487.
  • M. Kepczyk and E. R. Puczylowski, On radicals of rings which are sums of two subrings, Arc. Math. (Basel), 66(1) (1996), 8-12.
  • M. Kepczyk and E. R. Puczylowski, Rings which are sums of two subrings, Ring Theory (Miskolc, 1996), J. Pure App. Algebra, 133(1-2) (1998), 151-162.
  • M. Kepczyk and E. R. Puczylowski, Rings which are sums of two subrings satisfying polynomial identities, Comm. Algebra, 29(5) (2001), 2059-2065.
  • M. Kepczyk and E. R. Puczylowski, On the structure of rings which are sums of two subrings, Arc. Math. (Basel), 83(5) (2004), 429-436.
  • G. Kothe, Die Struktur der Ringe, deren Restklassenring nach dem Radikal vollstanding irreduzibel ist., Math. Z., 32 (1930), 161-186.
  • A. Smoktunowicz, On some results related to Kothe's conjecture, Serdica Math. J., 27 (2001), 159-170.
  • A. Smoktunowicz, A simple nil ring exists, Comm. Algebra, 30(1) (2002), 27- 59.
  • B. Stenstrom, Rings of Quotients: Die Grundlehren der Mathematischen Wissenschaften, Band 217, An introduction to methods of ring theory, Springer- Verlag, New York-Heidelberg, 1975.
There are 17 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

M. Tamer Kosan

Jan Zemlicka This is me

Publication Date July 11, 2019
DOI https://doi.org/10.24330/ieja.587018
IZ https://izlik.org/JA56ZS48SA
Published in Issue Year 2019 Volume: 26 Issue: 26

Cite

APA Kosan, M. T., & Zemlicka, J. (2019). ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS. International Electronic Journal of Algebra, 26(26), 131-144. https://doi.org/10.24330/ieja.587018
AMA 1.Kosan MT, Zemlicka J. ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS. IEJA. 2019;26(26):131-144. doi:10.24330/ieja.587018
Chicago Kosan, M. Tamer, and Jan Zemlicka. 2019. “ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS”. International Electronic Journal of Algebra 26 (26): 131-44. https://doi.org/10.24330/ieja.587018.
EndNote Kosan MT, Zemlicka J (July 1, 2019) ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS. International Electronic Journal of Algebra 26 26 131–144.
IEEE [1]M. T. Kosan and J. Zemlicka, “ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS”, IEJA, vol. 26, no. 26, pp. 131–144, July 2019, doi: 10.24330/ieja.587018.
ISNAD Kosan, M. Tamer - Zemlicka, Jan. “ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS”. International Electronic Journal of Algebra 26/26 (July 1, 2019): 131-144. https://doi.org/10.24330/ieja.587018.
JAMA 1.Kosan MT, Zemlicka J. ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS. IEJA. 2019;26:131–144.
MLA Kosan, M. Tamer, and Jan Zemlicka. “ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS”. International Electronic Journal of Algebra, vol. 26, no. 26, July 2019, pp. 131-44, doi:10.24330/ieja.587018.
Vancouver 1.M. Tamer Kosan, Jan Zemlicka. ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS. IEJA. 2019 Jul. 1;26(26):131-44. doi:10.24330/ieja.587018