Geodesic
On 2-primal Ore extensions over Noetherian σ(∗)-rings
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2011), pp. 42-49.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this article, we discuss the prime radical of skew polynomial rings over Noetherian rings. We recall σ(∗) property on a ring R (i.e. aσ(a)∈P(R) implies a∈P(R) for a∈R, where P(R) is the prime radical of R, and σ an automorphism of R). Let now δ be a σ-derivation of R such that δ(σ(a))=σ(δ(a)) for all a∈R. Then we show that for a Noetherian σ(∗)-ring, which is also an algebra over Q, the Ore extension R[x;σ,δ] is 2-primal Noetherian (i.e. the nil radical and the prime radical of R[x;σ,δ] coincide). 
@article{BASM_2011_1_a3,
     author = {Vijay Kumar Bhat},
     title = {On 2-primal {Ore} extensions over {Noetherian} $\sigma(*)$-rings},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {42--49},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2011_1_a3/}
}
TY  - JOUR
AU  - Vijay Kumar Bhat
TI  - On 2-primal Ore extensions over Noetherian $\sigma(*)$-rings
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2011
SP  - 42
EP  - 49
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2011_1_a3/
LA  - en
ID  - BASM_2011_1_a3
ER  - 
%0 Journal Article
%A Vijay Kumar Bhat
%T On 2-primal Ore extensions over Noetherian $\sigma(*)$-rings
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2011
%P 42-49
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2011_1_a3/
%G en
%F BASM_2011_1_a3
Vijay Kumar Bhat. On 2-primal Ore extensions over Noetherian $\sigma(*)$-rings. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2011), pp. 42-49. https://geodesic-test.mathdoc.fr/item/BASM_2011_1_a3/

[1] Argac N., Groenewald N. J., “A generalization of 2-primal near rings”, Quaest. Math., 27:4 (2004), 397–413 | DOI | MR | Zbl

[2] Bhat V. K., “On 2-primal Ore extensions”, Ukr. Math. Bull., 4:2 (2007), 173–179 | MR

[3] Bhat V. K., “Differential operator rings over 2-primal rings”, Ukr. Math. Bull., 5:2 (2008), 153–158 | MR

[4] Bhat V. K., Kumari Neetu, “Transparency of $\sigma(*)$-Rings and Their Extensions”, Int. J. Algebra, 2:19 (2008), 919–924 | MR | Zbl

[5] Bhat V. K., “Ore extensions over 2-primal Noetharian rings”, Bul. Acad. Stiinte Repub. Mold. Mat., 2008, no. 3(58), 34–43 | MR | Zbl

[6] Bhat V. K., “Associated prime ideals of skew polynomial rings”, Beitrage Algebra Geom., 49:1 (2008), 277–283 | MR | Zbl

[7] Bhat V. K., “On Near Pseudo-valuation rings and their extensions”, Int. Electron. J. Algebra, 5 (2009), 70–77 | MR | Zbl

[8] Blair W. D., Small L. W., “Embedding differential and skew-polynomial rings into artinain rings”, Proc. Amer. Math. Soc., 109:4 (1990), 881–886 | DOI | MR | Zbl

[9] Goodearl K. R., “Prime Ideals in Skew Polynomial Rings and Ouantized Weyl Algebras”, J. Algebra, 150 (1992), 324–377 | DOI | MR | Zbl

[10] Goodearl K. R., Warfield (Jr.) R. B., An introduction to non-commutative Noetherian rings, Cambridge Uni. Press, 1989 | Zbl

[11] Kim N. K., Kwak T. K., “Minimal prime ideals in 2-primal rings”, Math. Japon., 50:3 (1999), 415–420 | MR | Zbl

[12] Krempa J., “Some examples of reduced rings”, Algebra Colloq., 3:4 (1996), 289–300 | MR | Zbl

[13] Kwak T. K., “Prime radicals of skew-polynomial rings”, Int. J. Math. Sci., 2:2 (2003), 219–227 | MR | Zbl

[14] Marks G., “On 2-primal Ore extensions”, Comm. Algebra, 29:5 (2001), 2113–2123 | DOI | MR | Zbl

[15] McConnell J. C., Robson J. C., Noncommutative Noetherian Rings, Wiley, 1987 ; Revised edition, Amer. Math. Soc., 2001 | MR | Zbl | Zbl

[16] Seidenberg A., “Differential ideals in rings of finitely generated type”, Amer. J. Math., 89 (1967), 22–42 | DOI | MR | Zbl