## Taiwanese Journal of Mathematics

### ON JACOBSON PROPERTY OF $\Gamma_N$-RINGS

Dingguo Wang

#### Abstract

Let $M$ be a $\Gamma$-ring in the sense of Nobusawa. The ring $M_2=\left (\begin{array}{ll} R~~& \Gamma\\ M& \Gamma\\ \end{array}\right )$ was defined by Kyuno. Let $\cal{P}$ be a class of prime rings such that for every prime ring $R$ and any $0\neq e^2=e\in R,~R\in \cal{P}$ if and only if $eRe\in \cal{P}$. In this paper, the $\cal{P}$-Jacobson $\Gamma$-rings which include the Jacobson property and Brown-McCoy property as special case are defined. Relationships between $\cal{P}$-Jacobson properties of $\Gamma$-ring $M$ and the corresponding properties of $\Gamma_{n,m}$-ring $M_{m,n}$, the right operator ring $R$ of $\Gamma$-ring $M,~M$-ring $\Gamma$ and the ring $M_2$ are established.

#### Article information

Source
Taiwanese J. Math., Volume 1, Number 2 (1997), 159-170.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405234

Digital Object Identifier
doi:10.11650/twjm/1500405234

Mathematical Reviews number (MathSciNet)
MR1452093

Zentralblatt MATH identifier
0879.16033

Subjects
Primary: 16Y99: None of the above, but in this section

#### Citation

Wang, Dingguo. ON JACOBSON PROPERTY OF $\Gamma_N$-RINGS. Taiwanese J. Math. 1 (1997), no. 2, 159--170. doi:10.11650/twjm/1500405234. https://projecteuclid.org/euclid.twjm/1500405234