|
|
- 2015
约化环上矩阵环的一类拟Armendariz子环
|
Abstract:
摘要： 讨论了reduced环上n阶矩阵环Mn(R)的一类特殊拟Armendariz子环Sn(R).证明了如果R是reduced环,α2,…,αn是R的相容自同态,那么Sn(R)是拟Armendariz环.
Abstract: A class of special quasi-Armendariz subrings Sn(R) of the n×n matrix ring Mn(R) over a reduced ring is investigated. It is shown that Sn(R) is a quasi-Armendariz ring if R is a reduced ring with compatible endomorphisms α2,…,αn
| [1] | HIRANO Y. On annihilator ideals of a polynomial ring over a noncommutative ring[J]. J Pure Appl Algebra, 2002, 168:45-52. |
| [2] | HASHEMI E. Quasi-Armendariz rings relative to a monoid[J]. J Pure Appl Algebra, 2007, 211:374-382. |
| [3] | ANNIN S. Associated primes over skew polynomial rings[J]. Comm Algebra, 2002, 30(5):2511-2528. |
| [4] | REGE M B, CHHAWCHHARIA S. Armendariz rings[J]. Proc Japan Acad: Ser A, 1997, 73(1):14-17. |
| [5] | KWAK T K, LEE Y, YUN S J. The Armendariz property on ideals[J]. J Algebra, 2012, 354:121-135. |
| [6] | ANTOINE R. Examples of Armendariz rings[J]. Comm Algebra, 2002, 38(11):4130-4143. |
| [7] | LIU Zhongkui, QIAO Husheng. Generalized pp and zip subrings of matrix rings[J]. Communications in Mathematical Research, 2010, 26(3):193-202. |
| [8] | ANDERSON D D, CAMILLO V. Armendariz rings and Gaussian rings[J]. Comm Algebra, 1998, 26(7):2265-2272. |
| [9] | LEE T K, ZHOU Y. Armendariz and reduced rings[J]. Comm Algebra, 2004, 32(6):2287-2299. |
| [10] | NASR-ISFAHANI A R. Radicals of skew polynomial and skew laurent polynomial rings over skew Armendariz rings[J]. Comm Algebra, 2014, 42(3):1337-1349. |
| [11] | BASER M, KAYNARCA F, KWAK T K, et al. Weak quasi-Armendariz rings[J]. Algebra Colloq, 2011, 18(4):541-552. |
