|
Сибирские электронные математические известия, 2009, том 6, страницы 505–509
(Mi semr78)
|
|
|
|
Статьи
A note on σ(∗)-rings and their extensions
V. K. Bhat, Neetu Kumari School of Mathematics, SMVD University, Katra, India
Аннотация:
Let R be an associative ring with identity 1≠0, and σ an endomorphism of R. We recall
σ(∗) property on R (i.e. aσ(a)∈P(R) implies a∈P(R) for a∈R, where P(R) is the prime radical of R). Also recall that a ring R is said to be 2-primal if and only if the prime radical P(R) and nil radical are same, i.e. if the prime radical is a completely semiprime ideal. It can be seen that a σ(∗) ring is a 2-primal ring.
Let R be a ring and σ an automorphism of R. Then we know that σ can be extended to an automorphism of the skew polynomial ring R[x;σ]. In this paper we show that if R is
a Noetherian ring and σ is an automorphism of R such that R is a σ(∗)-ring, then
R[x;σ] is also a σ(∗)-ring.
Ключевые слова:
minimal prime, prime radical, automorphism, σ(∗)-ring.
Поступила 6 августа 2009 г., опубликована 27 ноября 2009 г.
Образец цитирования:
V. K. Bhat, Neetu Kumari, “A note on σ(∗)-rings and their extensions”, Сиб. электрон. матем. изв., 6 (2009), 505–509
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr78 https://www.mathnet.ru/rus/semr/v6/p505
|
|