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ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS

Yıl 2019, Cilt: 26 Sayı: 26, 131 - 144, 11.07.2019

M. Tamer Kosan Jan Zemlicka

https://doi.org/10.24330/ieja.587018

Öz

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).

Anahtar Kelimeler

Sum of rings sum of algebras

Kaynakça

  • 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.

Yıl 2019, Cilt: 26 Sayı: 26, 131 - 144, 11.07.2019

M. Tamer Kosan Jan Zemlicka

https://doi.org/10.24330/ieja.587018

Öz

Kaynakça

  • 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.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

M. Tamer Kosan

Jan Zemlicka Bu kişi benim

Yayımlanma Tarihi 11 Temmuz 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 26 Sayı: 26

Kaynak Göster

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. Temmuz 2019;26(26):131-144. doi:10.24330/ieja.587018
Chicago Kosan, M. Tamer, ve Jan Zemlicka. “ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS”. International Electronic Journal of Algebra 26, sy. 26 (Temmuz 2019): 131-44. https://doi.org/10.24330/ieja.587018.
EndNote Kosan MT, Zemlicka J (01 Temmuz 2019) ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS. International Electronic Journal of Algebra 26 26 131–144.
IEEE M. T. Kosan ve J. Zemlicka, “ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS”, IEJA, c. 26, sy. 26, ss. 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 (Temmuz 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 ve Jan Zemlicka. “ON FINITE DIMENSIONAL ALGEBRAS WHICH ARE SUMS OF TWO SUBALGEBRAS”. International Electronic Journal of Algebra, c. 26, sy. 26, 2019, ss. 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.