Large Free Algebras in the Ring of Fractions of Skew Polynomial Rings

1999 ◽  
Vol 60 (2) ◽  
pp. 481-489 ◽  
Author(s):  
M. Shirvani ◽  
J. Z. Gonçalves
Keyword(s):  
Polynomial Rings ◽  
Free Algebras ◽  
Skew Polynomial Rings ◽  
Ring Of Fractions ◽  
Skew Polynomial

Partial Skew Polynomial Rings Over Semisimple Artinian Rings

2010 ◽  
Vol 38 (5) ◽  
pp. 1663-1676 ◽  
Author(s):  
Wagner Cortes ◽  
Miguel Ferrero ◽  
Yasuyuki Hirano ◽  
Hidetoshi Marubayashi
Keyword(s):  
Polynomial Rings ◽  
Artinian Rings ◽  
Skew Polynomial Rings ◽  
Skew Polynomial

ANNIHILATOR CONDITIONS IN MATRIX AND SKEW POLYNOMIAL RINGS

2012 ◽  
Vol 11 (04) ◽  
pp. 1250079 ◽  
Author(s):  
A. ALHEVAZ ◽  
A. MOUSSAVI
Keyword(s):  
Polynomial Rings ◽  
Trivial Extension ◽  
Skew Polynomial Ring ◽  
Matrix Rings ◽  
Skew Polynomial Rings ◽  
Armendariz Rings ◽  
Ore Extensions ◽  
Necessary And Sufficient ◽  
Skew Polynomial ◽  
Armendariz Ring

Let R be a ring with an endomorphism α and α-derivation δ. By [A. R. Nasr-Isfahani and A. Moussavi, Ore extensions of skew Armendariz rings, Comm. Algebra 36(2) (2008) 508–522], a ring R is called a skew Armendariz ring, if for polynomials f(x) = a0 + a1 x + ⋯ + anxn, g(x) = b0+b1x + ⋯ + bmxm in R[x; α, δ], f(x)g(x) = 0 implies a0bj = 0 for each 0 ≤ j ≤ m. In this paper, radicals of the skew polynomial ring R[x; α, δ], in terms of a skew Armendariz ring R, is determined. We prove that several properties transfer between R and R[x; α, δ], in case R is an α-compatible skew Armendariz ring. We also identify some "relatively maximal" skew Armendariz subrings of matrix rings, and obtain a necessary and sufficient condition for a trivial extension to be skew Armendariz. Consequently, new families of non-reduced skew Armendariz rings are presented and several known results related to Armendariz rings and skew polynomial rings will be extended and unified.

scholarly journals SKEW POLYNOMIAL RINGS SATISFYING $R$-BND PROPERTY

1992 ◽  
Vol 23 (2) ◽  
pp. 109-116
Author(s):  
REFAAT M. SALEM
Keyword(s):  
Noetherian Ring ◽  
Polynomial Rings ◽  
Skew Polynomial Rings ◽  
Skew Polynomial

In this paper we show that, a prime right Noetherian ring $A$ satisfies $T(A) = n <\infty$ iff $A[x, \sigma]$ satisfies $r$-Bnd $(n + 1)$.

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