|
|
- 2015
幂零p.p.-环和幂零Baer环的Ore扩张
|
Abstract:
摘要： 研究环的Ore扩张的幂零p.p.性,幂零Baer性和弱McCoy性,主要证明了:设R是一个拟IFP和(α,δ)-condition环,则有(1)如果R是幂零p.p.-环,则R[x;α,δ]是幂零p.p.-环; (2)如果R是幂零Baer环,则 R[x;α,δ]是幂零Baer环; (3)R[x;α,δ]是右弱McCoy环.
Abstract: The nilpotent p.p., nilpotent Baer and weak McCoy property of the Ore extensions of a ring are investigated. Let R be a quasi-IFP and (α,δ)-condition ring. It is mainly shown that (1) if R is a nilpotent p.p.-ring, then R[x;α,δ] is a nilpotent p.p.-ring; (2) if R is a nilpotent Baer ring, then R[x;α,δ] is a nilpotent Baer ring; (3) R[x;α,δ] is a weak McCoy ring
| [1] | ARMENDARIZ E P. A note on extensions of Baer and p.p.-rings[J]. J Austral Math Soc, 1974, 18:470-473. |
| [2] | HONG C Y, KIM N K, KWAK T K. Ore extensions of Baer and p.p.-rings[J]. J Pure Appl Algebra, 2000, 151:215-226. |
| [3] | MOHAMMADI R, MOUSSAVI A, ZAHIRI M. On weak zip skew polynomial rings[J]. Asian European J Math, 2012, 5(3):3901-3917. |
| [4] | GHALANDARZADEH Sh, KHORAMDEL M. On weak McCoy rings[J]. Thai J Math, 2008, 6(2):337-342. |
| [5] | BIRKENMEIER G F, KIM J Y, PARK J K. Polynomial extensions of Baer and quasi-Bear-rings[J]. J Pure Appl Algebra, 2001, 159:25-42. |
| [6] | KIM N K, LEE Y. Extensions of reversible rings[J]. J Pure Appl Algebra, 2003, 185:207-223. |
| [7] | KIM H K, KIM N K, JEONG M S, et al. On conditions provided by nilradicals[J]. J Korean Math Soc, 2009, 46(5):1027-1040. |
| [8] | MOHAMMADI R, MOUSSAVI A, ZAHIRI M. Weak McCoy ore extensions[J]. Int Math Forum, 2011, 6(2):75-86. |
