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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

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

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 Articles
Authors

M. Tamer Kosan

Jan Zemlicka This is me

Publication Date July 11, 2019
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 Kosan MT, Zemlicka J. ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS. IEJA. July 2019;26(26):131-144. doi:10.24330/ieja.587018
Chicago Kosan, M. Tamer, and Jan Zemlicka. “ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS”. International Electronic Journal of Algebra 26, no. 26 (July 2019): 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 M. T. Kosan and J. Zemlicka, “ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS”, IEJA, vol. 26, no. 26, pp. 131–144, 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 2019), 131-144. https://doi.org/10.24330/ieja.587018.
JAMA 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, 2019, pp. 131-44, doi:10.24330/ieja.587018.
Vancouver Kosan MT, Zemlicka J. ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS. IEJA. 2019;26(26):131-44.