Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2024, Cilt: 36 Sayı: 36, 66 - 72, 12.07.2024
https://doi.org/10.24330/ieja.1438742

Öz

Kaynakça

  • I. N. Herstein, Noncommutative Rings, Carus Math. Monogr., 15, Mathematical Association of America, Washington, DC, 1994.
  • N. Jacobson, A Kronecker factorization theorem for Cayley algebras and the exceptional simple Jordan algebra, Amer. J. Math., 76 (1954), 447-452.
  • N. Jacobson, Structure and Representations of Jordan Algebras, Amer. Math. Soc. Colloq. Publ., American Mathematical Society, Providence, RI, 1968.
  • N. Jacobson, Basic Algebra II, W. H. Freeman and Co., San Francisco, CA, 1980.
  • I. Kaplansky, Semi-simple alternative rings, Portugal. Math., 10 (1951), 37-50.
  • M. C. López-Díaz and I. P. Shestakov, Representations of exceptional simple alternative superalgebras of characteristic 3, Trans. Amer. Math. Soc., 354(7) (2002), 2745-2758.
  • M. C. López-Díaz and I. P. Shestakov, Representations of exceptional simple Jordan superalgebras of characteristic 3, Comm. Algebra, 33(1) (2005), 331-337.
  • V. H. López Solís, Kronecker factorization theorems for alternative superalgebras, J. Algebra, 528 (2019), 311-338.
  • V. H. López Solís, On a problem by Nathan Jacobson for Malcev algebras, arXiv:2106.01155.
  • V. H. López Solís, Kronecker factorization theorems for the exceptional Malcev algebra, Preprint.
  • V. H. López Solís and I. P. Shestakov, On a problem by Nathan Jacobson, Rev. Mat. Iberoam., 38(4) (2022), 1219-1238.
  • C. Martínez and E. Zelmanov, A Kronecker factorization theorem for the exceptional Jordan superalgebra, J. Pure Appl. Algebra, 177(1) (2003), 71-78.
  • K. McCrimmon, A Taste of Jordan Algebras, Universitext, Springer-Verlag, New York, 2004.
  • S. V. Pchelintsev, O. V. Shashkov and I. P. Shestakov, Right alternative bimodules over Cayley algebra and coordinatization theorem, J. Algebra, 572 (2021), 111-128.
  • M. A. Yglesias Jauregui, V. H. López Solís, B. M. Cerna Maguiña and V. A. Pocoy Yauri, Bimódulos asociativos unitarios irreducibles sobre la álgebra de las matrices $n\times n$, https://repositorio.unasam.edu.pe/handle/UNASAM/4736, (2018).

A categories equivalence of associative bimodules

Yıl 2024, Cilt: 36 Sayı: 36, 66 - 72, 12.07.2024
https://doi.org/10.24330/ieja.1438742

Öz

In this paper we use the classical Wedderburn's Kronecker Factorization Theorem to prove that category of bimodules over $B$ and the category of bimodules over $M_{n}(B)$ are equivalent, where $B$ is some unital associative algebra. In addition to this, we classify the irreducible bimodules over $M_{n}(F).$

Kaynakça

  • I. N. Herstein, Noncommutative Rings, Carus Math. Monogr., 15, Mathematical Association of America, Washington, DC, 1994.
  • N. Jacobson, A Kronecker factorization theorem for Cayley algebras and the exceptional simple Jordan algebra, Amer. J. Math., 76 (1954), 447-452.
  • N. Jacobson, Structure and Representations of Jordan Algebras, Amer. Math. Soc. Colloq. Publ., American Mathematical Society, Providence, RI, 1968.
  • N. Jacobson, Basic Algebra II, W. H. Freeman and Co., San Francisco, CA, 1980.
  • I. Kaplansky, Semi-simple alternative rings, Portugal. Math., 10 (1951), 37-50.
  • M. C. López-Díaz and I. P. Shestakov, Representations of exceptional simple alternative superalgebras of characteristic 3, Trans. Amer. Math. Soc., 354(7) (2002), 2745-2758.
  • M. C. López-Díaz and I. P. Shestakov, Representations of exceptional simple Jordan superalgebras of characteristic 3, Comm. Algebra, 33(1) (2005), 331-337.
  • V. H. López Solís, Kronecker factorization theorems for alternative superalgebras, J. Algebra, 528 (2019), 311-338.
  • V. H. López Solís, On a problem by Nathan Jacobson for Malcev algebras, arXiv:2106.01155.
  • V. H. López Solís, Kronecker factorization theorems for the exceptional Malcev algebra, Preprint.
  • V. H. López Solís and I. P. Shestakov, On a problem by Nathan Jacobson, Rev. Mat. Iberoam., 38(4) (2022), 1219-1238.
  • C. Martínez and E. Zelmanov, A Kronecker factorization theorem for the exceptional Jordan superalgebra, J. Pure Appl. Algebra, 177(1) (2003), 71-78.
  • K. McCrimmon, A Taste of Jordan Algebras, Universitext, Springer-Verlag, New York, 2004.
  • S. V. Pchelintsev, O. V. Shashkov and I. P. Shestakov, Right alternative bimodules over Cayley algebra and coordinatization theorem, J. Algebra, 572 (2021), 111-128.
  • M. A. Yglesias Jauregui, V. H. López Solís, B. M. Cerna Maguiña and V. A. Pocoy Yauri, Bimódulos asociativos unitarios irreducibles sobre la álgebra de las matrices $n\times n$, https://repositorio.unasam.edu.pe/handle/UNASAM/4736, (2018).
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi
Bölüm Makaleler
Yazarlar

Victor López Solís

Marlennhi Moreno Vıllanueva Bu kişi benim

Erken Görünüm Tarihi 17 Şubat 2024
Yayımlanma Tarihi 12 Temmuz 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 36 Sayı: 36

Kaynak Göster

APA López Solís, V., & Moreno Vıllanueva, M. (2024). A categories equivalence of associative bimodules. International Electronic Journal of Algebra, 36(36), 66-72. https://doi.org/10.24330/ieja.1438742
AMA López Solís V, Moreno Vıllanueva M. A categories equivalence of associative bimodules. IEJA. Temmuz 2024;36(36):66-72. doi:10.24330/ieja.1438742
Chicago López Solís, Victor, ve Marlennhi Moreno Vıllanueva. “A Categories Equivalence of Associative Bimodules”. International Electronic Journal of Algebra 36, sy. 36 (Temmuz 2024): 66-72. https://doi.org/10.24330/ieja.1438742.
EndNote López Solís V, Moreno Vıllanueva M (01 Temmuz 2024) A categories equivalence of associative bimodules. International Electronic Journal of Algebra 36 36 66–72.
IEEE V. López Solís ve M. Moreno Vıllanueva, “A categories equivalence of associative bimodules”, IEJA, c. 36, sy. 36, ss. 66–72, 2024, doi: 10.24330/ieja.1438742.
ISNAD López Solís, Victor - Moreno Vıllanueva, Marlennhi. “A Categories Equivalence of Associative Bimodules”. International Electronic Journal of Algebra 36/36 (Temmuz 2024), 66-72. https://doi.org/10.24330/ieja.1438742.
JAMA López Solís V, Moreno Vıllanueva M. A categories equivalence of associative bimodules. IEJA. 2024;36:66–72.
MLA López Solís, Victor ve Marlennhi Moreno Vıllanueva. “A Categories Equivalence of Associative Bimodules”. International Electronic Journal of Algebra, c. 36, sy. 36, 2024, ss. 66-72, doi:10.24330/ieja.1438742.
Vancouver López Solís V, Moreno Vıllanueva M. A categories equivalence of associative bimodules. IEJA. 2024;36(36):66-72.