Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2025, Early Access, 1 - 29

Basudeb Dhara , Vincenzo De Filippis , S. Kar , Manami Bera

https://doi.org/10.24330/ieja.1646846

Öz

Kaynakça

  • N. Bera and B. Dhara, $b$-generalized skew derivations acting on multilinear polynomials in prime rings, Comm. Algebra, 53(2) (2025), 761-780.
  • C.-L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc., 103(3) (1988), 723-728.
  • V. De Filippis and O. M. Di Vincenzo, Vanishing derivations and centralizers of generalized derivations on multilinear polynomials, Comm. Algebra, 40(6) (2012), 1918-1932.
  • B. Dhara, $b$-Generalized derivations on multilinear polynomials in prime rings, Bull. Korean Math. Soc., 55(2) (2018), 573-586.
  • B. Dhara, Generalized derivations acting on multilinear polynomials in prime rings, Czechoslovak Math. J., 68(1) (2018), 95-119.
  • B. Dhara and N. Argac, Generalized derivations acting on multilinear polynomials in prime rings and Banach algebras, Commun. Math. Stat., 4(1) (2016), 39-54.
  • B. Dhara and V. De Filippis, $b$-Generalized derivations acting on multilinear polynomials in prime rings, Algebra Colloq., 25(4) (2018), 681-700.
  • T. S. Erickson, W. S. Martindale, III and J. M. Osborn, Prime nonassociative algebras, Pacific J. Math., 60(1) (1975), 49-63.
  • C. Faith and Y. Utumi, On a new proof of Litoff's theorem, Acta Math. Acad. Sci. Hungar., 14 (1963), 369-371.
  • C. Gupta, On $b$-generalized derivations in prime rings, Rend. Circ. Mat. Palermo, (2), 72(4) (2023), 2703-2720.
  • N. Jacobson, Structure of Rings, Amer. Math. Soc. Colloq. Pub., 37, Amer. Math. Soc., Providence, RI, 1964.
  • V. K. Kharchenko, Differential identities of prime rings, Algebra Logic, 17 (1978), 155-168.
  • M. T. Kosan and T. K. Lee, $b$-Generalized derivations of semiprime rings having nilpotent values, J. Aust. Math. Soc., 96(3) (2014), 326-337.
  • T. K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica, 20(1) (1992), 27-38.
  • U. Leron, Nil and power-central polynomials in rings, Trans. Amer. Math. Soc., 202 (1975), 97-103.
  • C.-K. Liu, An Engel condition with b-generalized derivations, Linear Multilinear Algebra, 65(2) (2017), 300-312.
  • W. S. Martindale, III, Prime rings satisfying a generalized polynomial identity, J. Algebra, 12 (1969), 576-584.
  • T. Pehlivan and E. Albas, $b$-Generalized derivations on prime rings, Ukrainian Math. J., 74(6) (2022), 953-966.
  • B. Prajapati, S. K. Tiwari and C. Gupta, $b$-generalized derivations act as a multipliers on prime rings, Comm. Algebra, 50(8) (2022), 3498-3515.
  • S. K. Tiwari, Identities with generalized derivations in prime rings, Rend. Circ. Mat. Palermo, (2), 71(1) (2022), 207-223.
  • S. K. Tiwari and B. Prajapati, Centralizing $b$-generalized derivations on multilinear polynomials, Filomat, 33(19) (2019), 6251-6266.
  • T.-L. Wong, Derivations with power central values on multilinear polynomials, Algebra Colloq., 3(4) (1996), 369-378.

Action of three $X$-generalized derivations in prime rings

Yıl 2025, Early Access, 1 - 29

Basudeb Dhara , Vincenzo De Filippis , S. Kar , Manami Bera

https://doi.org/10.24330/ieja.1646846

Öz

Let $\mathfrak{R}$ be a prime ring of characteristic different from $2$, $\mathcal{Q}_r^m$ be its maximal right ring of quotients, $\mathcal{C}$ be its extended centroid and $\omega(s_1,\ldots,s_n)$ be a noncentral multilinear polynomial over $\mathcal{C}$. Suppose that $\mathcal{H}_1$, $\mathcal{H}_2$ and $\mathcal{H}_3$ are three $X$-generalized derivations on $\mathfrak{R}$. If $$\mathcal{H}_1\bigg(\mathcal{H}_2(\omega(s_1,\ldots,s_n))\omega(s_1,\ldots,s_n)\bigg)=\mathcal{H}_3(\omega(s_1,\ldots,s_n)^2)$$ for all $s_1,\ldots,s_n\in \mathfrak{R}$, then we detail all potential configurations of the maps $\mathcal{H}_1, \mathcal{H}_2$ and $\mathcal{H}_3$.

Anahtar Kelimeler

Generalized derivation $X$-generalized derivation extended centroid multilinear polynomial prime ring

Kaynakça

  • N. Bera and B. Dhara, $b$-generalized skew derivations acting on multilinear polynomials in prime rings, Comm. Algebra, 53(2) (2025), 761-780.
  • C.-L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc., 103(3) (1988), 723-728.
  • V. De Filippis and O. M. Di Vincenzo, Vanishing derivations and centralizers of generalized derivations on multilinear polynomials, Comm. Algebra, 40(6) (2012), 1918-1932.
  • B. Dhara, $b$-Generalized derivations on multilinear polynomials in prime rings, Bull. Korean Math. Soc., 55(2) (2018), 573-586.
  • B. Dhara, Generalized derivations acting on multilinear polynomials in prime rings, Czechoslovak Math. J., 68(1) (2018), 95-119.
  • B. Dhara and N. Argac, Generalized derivations acting on multilinear polynomials in prime rings and Banach algebras, Commun. Math. Stat., 4(1) (2016), 39-54.
  • B. Dhara and V. De Filippis, $b$-Generalized derivations acting on multilinear polynomials in prime rings, Algebra Colloq., 25(4) (2018), 681-700.
  • T. S. Erickson, W. S. Martindale, III and J. M. Osborn, Prime nonassociative algebras, Pacific J. Math., 60(1) (1975), 49-63.
  • C. Faith and Y. Utumi, On a new proof of Litoff's theorem, Acta Math. Acad. Sci. Hungar., 14 (1963), 369-371.
  • C. Gupta, On $b$-generalized derivations in prime rings, Rend. Circ. Mat. Palermo, (2), 72(4) (2023), 2703-2720.
  • N. Jacobson, Structure of Rings, Amer. Math. Soc. Colloq. Pub., 37, Amer. Math. Soc., Providence, RI, 1964.
  • V. K. Kharchenko, Differential identities of prime rings, Algebra Logic, 17 (1978), 155-168.
  • M. T. Kosan and T. K. Lee, $b$-Generalized derivations of semiprime rings having nilpotent values, J. Aust. Math. Soc., 96(3) (2014), 326-337.
  • T. K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica, 20(1) (1992), 27-38.
  • U. Leron, Nil and power-central polynomials in rings, Trans. Amer. Math. Soc., 202 (1975), 97-103.
  • C.-K. Liu, An Engel condition with b-generalized derivations, Linear Multilinear Algebra, 65(2) (2017), 300-312.
  • W. S. Martindale, III, Prime rings satisfying a generalized polynomial identity, J. Algebra, 12 (1969), 576-584.
  • T. Pehlivan and E. Albas, $b$-Generalized derivations on prime rings, Ukrainian Math. J., 74(6) (2022), 953-966.
  • B. Prajapati, S. K. Tiwari and C. Gupta, $b$-generalized derivations act as a multipliers on prime rings, Comm. Algebra, 50(8) (2022), 3498-3515.
  • S. K. Tiwari, Identities with generalized derivations in prime rings, Rend. Circ. Mat. Palermo, (2), 71(1) (2022), 207-223.
  • S. K. Tiwari and B. Prajapati, Centralizing $b$-generalized derivations on multilinear polynomials, Filomat, 33(19) (2019), 6251-6266.
  • T.-L. Wong, Derivations with power central values on multilinear polynomials, Algebra Colloq., 3(4) (1996), 369-378.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi
Bölüm Makaleler
Yazarlar

Basudeb Dhara

Vincenzo De Filippis

S. Kar

Manami Bera

Erken Görünüm Tarihi 25 Şubat 2025
Yayımlanma Tarihi
Gönderilme Tarihi 3 Eylül 2024
Kabul Tarihi 25 Ocak 2025
Yayımlandığı Sayı Yıl 2025 Early Access

Kaynak Göster

APA Dhara, B., De Filippis, V., Kar, S., Bera, M. (2025). Action of three $X$-generalized derivations in prime rings. International Electronic Journal of Algebra1-29. https://doi.org/10.24330/ieja.1646846
AMA Dhara B, De Filippis V, Kar S, Bera M. Action of three $X$-generalized derivations in prime rings. IEJA. Published online 01 Şubat 2025:1-29. doi:10.24330/ieja.1646846
Chicago Dhara, Basudeb, Vincenzo De Filippis, S. Kar, ve Manami Bera. “Action of Three $X$-Generalized Derivations in Prime Rings”. International Electronic Journal of Algebra, Şubat (Şubat 2025), 1-29. https://doi.org/10.24330/ieja.1646846.
EndNote Dhara B, De Filippis V, Kar S, Bera M (01 Şubat 2025) Action of three $X$-generalized derivations in prime rings. International Electronic Journal of Algebra 1–29.
IEEE B. Dhara, V. De Filippis, S. Kar, ve M. Bera, “Action of three $X$-generalized derivations in prime rings”, IEJA, ss. 1–29, Şubat 2025, doi: 10.24330/ieja.1646846.
ISNAD Dhara, Basudeb vd. “Action of Three $X$-Generalized Derivations in Prime Rings”. International Electronic Journal of Algebra. Şubat 2025. 1-29. https://doi.org/10.24330/ieja.1646846.
JAMA Dhara B, De Filippis V, Kar S, Bera M. Action of three $X$-generalized derivations in prime rings. IEJA. 2025;:1–29.
MLA Dhara, Basudeb vd. “Action of Three $X$-Generalized Derivations in Prime Rings”. International Electronic Journal of Algebra, 2025, ss. 1-29, doi:10.24330/ieja.1646846.
Vancouver Dhara B, De Filippis V, Kar S, Bera M. Action of three $X$-generalized derivations in prime rings. IEJA. 2025:1-29.